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Maths M.C.Q. [1 Marks Each]

Factorization · Jharkhand Board (JAC) STD 8 (Jharkhand - English Medium). 256 questions.

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M.C.Q. [1 Marks Each]

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256 questions · auto-graded multiple-choice test.

MCQ 11 Mark
The factors of $m^2 - 256$ are:
  • A
    $(m + 4)^2$
  • B
    $(m - 4)^2$
  • C
    $(m - 4) (m + 4)$
  • ✓
    None of the above.
Answer
Correct option: D.
None of the above.
$m^4 = (m^2)^2\ \  and\ \  256 = (16)^2$
$m^4 - 256 = (m^2)^2 - (16)^2 = (m^2 - 16) (m^2 + 16)$
$m^2 - 16 = m^2 - 4^2 = (m - 4) (m + 4)$
$m^4 - 256 = (m - 4) (m + 4) (m^2 + 16)$
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MCQ 21 Mark
The factors of $49p^2 - 36$ are:
  • ✓
    $(7p - 6) (7p + 6)$
  • B
    $(7p + 6)^2$
  • C
    $(7p - 6)^2$
  • D
    None of the above.
Answer
Correct option: A.
$(7p - 6) (7p + 6)$
a. $(7p - 6) (7p + 6)$
Solution:
$= 49p^2 - 36 = (7p)^2 – (6)^2$
$= (7p - 6) (7p + 6)$
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MCQ 31 Mark
The factorisation of $y^2 - 7y + 12$ is:
  • A
    $(y + 3) (y + 4)$
  • B
    $(y + 3) (y - 4)$
  • C
    $(y - 3) (y + 4)$
  • ✓
    $(y - 3) (y - 4)$
Answer
Correct option: D.
$(y - 3) (y - 4)$
$= y^2 - 7y + 12$
$= y^2 - 3y - 4y + 12$
$= y(y - 3) - 4(y - 3)$
$= (y - 3) (y - 4)$
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MCQ 41 Mark
The factorisation of $x^2 + 8x + 16$ is:
  • A
    $(x + 2)^2$
  • ✓
    $(x + 4)^2$
  • C
    $(x - 2)^2$
  • D
    $(x - A)^2$
Answer
Correct option: B.
$(x + 4)^2$
$= x^2 + 8x + 16$
$= (x)^2 + 2 (x) (4) + (4)^2$
$= (x + 4)^2$
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MCQ 51 Mark
The factors of $3m^2 + 9m + 6$ are:
  • A
    $(m + 1) (m + 2)$
  • ✓
    $3(m + 1) (m + 2)$
  • C
    $6(m + 1) (m + 2)$
  • D
    $9(m + 1) (m + 2)$
Answer
Correct option: B.
$3(m + 1) (m + 2)$
B.  $3(m + 1) (m + 2)$
Solution:
$= 3m^2 + 9m + 6 = 3(m^2 + 3m + 2)$
$= 3 (m^2 + m + 2m + 2)$
$= 3m(m + 1) + 2( m + 1)$
$= 3(m + 1) (m + 2)$
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MCQ 61 Mark
The factors of $6xy - 4y + 6 - 9x$ are:
  • A
    $(3x + 2) (2y + 3)$
  • B
    $(3x - 2) (2y + 3)$
  • C
    $(3x - +2) (2y - 3)$
  • ✓
    $(3x - 2) (2y - 3)$
Answer
Correct option: D.
$(3x - 2) (2y - 3)$
$= 6xy - 4y + 6 - 9x$
$= 6xy - 4y - 9x + 6$
$= 2y(3x - 2) - 3(3x - 2)$
$= (3x - 2) (2y - 3)$
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MCQ 71 Mark
The common factor $12a$ and $30$ is:
  • A
    $12$
  • ✓
    $6$
  • C
    $30$
  • D
    $6a$
Answer
Correct option: B.
$6$

$12a = 2 \times 2 \times 3 \times a$
$30 = 2 \times 3 \times 5$

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MCQ 81 Mark
Solve: $-20(x)^4 \div 10(x)^2$
  • A
    $\frac{1}{2\text{x}}$
  • B
    $\text{x}$
  • C
    $\frac{1}{2}$
  • ✓
    $-2\text{x}^2$
Answer
Correct option: D.
$-2\text{x}^2$
D.  $-2\text{x}^2$
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MCQ 91 Mark
If $(x^2 + 3x + 5) (x^2 - 3x + 5) = m^2 - n^2,$ what is the value of $m\ ?$
  • A
    $x^2 - 3x$
  • B
    $3x$
  • ✓
    $x^2 + 5$
  • D
    $x^2 + 3x$
Answer
Correct option: C.
$x^2 + 5$
C.  $x^2 + 5$
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MCQ 101 Mark
The value of $\frac{0.73\times0.73\times-0.27\times0.27}{0.73-0.27}$ is:
  • ✓
    $1$
  • B
    $0$
  • C
    $0.73$
  • D
    $0.27$
Answer
Correct option: A.
$1$
Value $=\frac{(0.73+0.27)(0.73-0.27)}{0.73-0.27}=1$
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MCQ 111 Mark
Divide $44(a^2 - 5a^3 - 50a^2)$ by $11a(a - 10)$
  • A
    $4a(a - 10)$
  • ✓
    $4a(a + 5)$
  • C
    $4a$
  • D
    $(a + 5) (a - 10)$
Answer
Correct option: B.
$4a(a + 5)$
B.  $4a(a + 5)$
Solution:
Write the division as a fraction
$\Rightarrow\frac{44(\text{a}^4-5\text{a}^3-50\text{a}^2)}{11\text{a}(\text{a}-10)}$
Find the factors of the numerator,
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}^2-5\text{a}-50)}{11\text{a}(\text{a}-10)}$
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}^2-10\text{a}+5\text{a}-50)}{11\text{a}(\text{a}-10)}$
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}(\text{a}-10)+5(\text{a}-10))}{11\text{a}(\text{a}-10)}$
$\Rightarrow\frac{11\times4\text{a}^2(\text{a}+5)(\text{a}-10)}{11\text{a}(\text{a}-10)}$
Cancel the common factors from the numerator and denominator.
$\Rightarrow4(\text{a}+5)$
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MCQ 121 Mark
The factors of $x^2 + xy - 2xz - 2yz$ are:
  • A
    $(x - y)(x + 2z)$
  • B
    $(x + y)(x + 2z)$
  • C
    $(x + y)(x + 2z)$
  • ✓
    $(x + y)(x - 2z)$
Answer
Correct option: D.
$(x + y)(x - 2z)$
D.  $(x + y)(x - 2z)$
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MCQ 131 Mark
Factorise: $x^2 + xy + 8x + 8y$
  • ✓
    $(x + 8) (x + y)$
  • B
    $(x + y)$
  • C
    $(x + 8)$
  • D
    $(x + 9) (x - y)$
Answer
Correct option: A.
$(x + 8) (x + y)$
A.  $(x + 8) (x + y)$
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MCQ 141 Mark
The factorisation of $6 - x - 2x^2$ is:
  • ✓
    $(2 + x) (3 - 2x)$
  • B
    $(2 + x) (3 + 2x)$
  • C
    $(2 - x) (3 - 2x)$
  • D
    $(2 - x) (3 + 2x)$
Answer
Correct option: A.
$(2 + x) (3 - 2x)$
A.  $(2 + x) (3 - 2x)$
Solution:
$= 6 - x - 2x^2$
$= 6 + 3x - 4x - 2x^2$
$= 3(2 + x) - 2x (2 + x)$
$= (2 + x) (3 - 2x)$
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MCQ 151 Mark
Factorize Completely $x^4 - 625$
  • ✓
    $(x \div 5) (x - 5) (x^2 \div 25)$
  • B
    $(x^2 - 25) (x^2 \div 5)$
  • C
    $(x \div 5)^2 (x - 5)$
  • D
    $(x \div 5) (x - 5)^2$
Answer
Correct option: A.
$(x \div 5) (x - 5) (x^2 \div 25)$
A.   $(x \div 5) (x - 5) (x^2 \div 25)$
Solution:
$x^4 - 625 = (x^2)^2 - (25)^2$
Apply the identity, $a^2 - b^2 = (a + b) (a - b)$
$\Rightarrow (x^2 + 25) (x^2 - 25)$
Factorize $(x^2 - 25)$ using the same identity.
$\Rightarrow (x^2 + 25) (x)^2 - (5)^2$
$\Rightarrow (x^2 + 25) (x + 5) (x - 5)$
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MCQ 161 Mark
The factorisation of $49p^2 - 36$ is:
  • ✓
    $(7p + 6) (7p - 6)$
  • B
    $(6p + 7) (6p - 7)$
  • C
    $(7p + 6)^2$
  • D
    $(7p - 6)^2$
Answer
Correct option: A.
$(7p + 6) (7p - 6)$
A.  $(7p + 6) (7p - 6)$
Solution:
$= 49p^2 - 36$
$= (7p)^2 - (6)^2$
$= (7p - 6) (7p + 6)$
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MCQ 171 Mark
One factor od $a^2 - c^2 + b^2$
  • A
    $(a + b + c)$
  • B
    $(a + b - c)$
  • ✓
    $(a - b + c)$
  • D
    None of these.
Answer
Correct option: C.
$(a - b + c)$
C.  $(a - b + c)$
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MCQ 181 Mark
Which of the following is quotient obtained on dividing $(x^2 - b)\  (x - a)$ by $-(x - a)\ ?$
  • A
    $(\text{x}^2 – \text{b})$
  • B
    $\frac{-(\text{x}^2 – \text{b})}{(\text{x}-\text{a})}$
  • ✓
    $-(\text{x}^2 – \text{b})$
  • D
    $-(\text{x}+\text{a})$
Answer
Correct option: C.
$-(\text{x}^2 – \text{b})$
C.  $-(\text{x}^2 – \text{b})$
Solution:
$(\text{x}^2-\text{b})(\text{x}-\text{a})$ By $-(\text{x}-\text{a})$
$\frac{(\text{x}^2-\text{b})(\text{x}-\text{a})}{-\text{x}-\text{a}}=\frac{\text{x}^2-\text{b}}{-(\text{x}-\text{a})}$
$=(\text{x}^2-\text{b)}$
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MCQ 191 Mark
The factors of $1 - p^3$ are:
  • A
    $(1 + p)(1 + p^2)$
  • ✓
    $(1- p)(1 + p + p^2)$
  • C
    $(1 + p)(1 - p - p^2)$
  • D
    $(1 + p)(1 - p^2)$
Answer
Correct option: B.
$(1- p)(1 + p + p^2)$
B.  $(1- p)(1 + p + p^2)$
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MCQ 201 Mark
The factors of $x^2 + xy + 8x + 8y$ are:
  • ✓
    $(x +y) (x + 8)$
  • B
    $(2x + y) (x + 8)$
  • C
    $(x + 2y) (x + 8)$
  • D
    $(x + y) (2x + 8)$
Answer
Correct option: A.
$(x +y) (x + 8)$
A.  $(x +y) (x + 8)$
Solution:
$= x^2 + xy + 8x + 8y$
$= x(x + y) + 8(x + y)$
$=(x + y) (x + 8)$
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MCQ 211 Mark
Tick $(\checkmark)$ the correct answer:
$x^3 - 144x = ?$
  • A
    $x(x - 12)^2$
  • B
    $x(x + 12)^2$
  • ✓
    $x(x - 12)(x + 12)$
  • D
    None of these
Answer
Correct option: C.
$x(x - 12)(x + 12)$
C.  $x(x - 12)(x + 12)$
Solution:
$x^3 - 144x$
$= x(x^2 - 144)$
$= x{(x)^2 - (12)^2}$
$= x(x - 12)(x + 12)$
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MCQ 221 Mark
Substitute $a = -3$ in $a^2 + 7a + 5$ and figure out it equals how much.
  • A
    $19$
  • B
    $24$
  • ✓
    $-7$
  • D
    $26$
Answer
Correct option: C.
$-7$
B.  $-7$
Solution:
Substitute $a = -3$ in $a^2 + 7a + 5$
$\Rightarrow (-3)^2 + 7(-3) +5$
$\Rightarrow 9 - 21 + 5$
$\Rightarrow 9 - 16$
$\Rightarrow -7$
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MCQ 231 Mark
The common factor of $72x^3y^4z^4, 120z^2d^4x^4$ and $96y^3z^4d^4$ is:
  • A
    $96z^3$
  • B
    $120z^3$
  • C
    $72z^3$
  • ✓
    $24z^2$
Answer
Correct option: D.
$24z^2$
D.  $24z^2$
Solution:
$72x^3y^4z^4 = 2 \times 2 \times 2 \times 3 \times 3 \times x \times x \times x \times y \times y \times y \times y \times z \times z \times z \times z$
$120z^2d^4x^4 = 2 \times 2 \times 2 \times 3 \times 5 \times z \times z \times d \times d \times d \times d \times x \times x \times x \times x$
$96y^3z^4d^4 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times y \times y \times z \times z \times z \times z \times d \times d \times d \times d$
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MCQ 241 Mark
Tick $(\checkmark)$ the correct answer:
$x^2 - xz + xy - yz =\  ?$
  • A
    $(x - y)(x + z)$
  • B
    $(x - y)(x - z)$
  • ✓
    $(x + y)(x - z)$
  • D
    $(x - y)(z - x)$
Answer
Correct option: C.
$(x + y)(x - z)$
C.  $(x + y)(x - z)$
Solution:
$x^2- xz + xy - yz$
$= x(x - z) + y(x - z)$
$= (x + y) (x - z)$
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MCQ 251 Mark
The factorisation of $12a^2b+15ab^2$ gives:
  • A
    $3ab(4ab + 5)$
  • ✓
    $3ab(4a + 5b)$
  • C
    $3a(4a + 5b)$
  • D
    $3b(4a + 5b)$
Answer
Correct option: B.
$3ab(4a + 5b)$
B.  $3 a b(4 a+5 b)$
Solution:
$12 a^2 b+15 a b^2 $
$12 a^2 b=3 \times 4 \times a \times a \times b $
$15 a b^2=3 \times 5 \times a \times b \times b$
The common factors are 3ab.
$12 a^2 b+15 a b^2=3 a b(4 a+5 b)$
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MCQ 261 Mark
The factorisation of $8x + 4y$ is:
  • ✓
    $4(2x + y)$
  • B
    $8(x + 4y)$
  • C
    $4(2x + 4y)$
  • D
    $8(x + y)$
Answer
Correct option: A.
$4(2x + y)$
$4(2x + y)$
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MCQ 271 Mark
Which of the following are the factors of $a^2 + ab + bc + ca,$
  • A
    $(b + c) (c + a)$
  • ✓
    $(a + b) (a + c)$
  • C
    $a (a + b + c)$
  • D
    $(a + b) (b + c)​$
Answer
Correct option: B.
$(a + b) (a + c)$
B.  $(a + b) (a + c)$
Solution:
$= a^2 + ab + bc + ca$
$= a (a + b) + c (b + a)$
$= a (a + b) + c (a + b)$
$= (a + b) (a + c)$
Therefore, the factors of $a^2 + ab + bc + ca$ are $(a + b) (a + c).$
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MCQ 281 Mark
If $(x^2 + 3x + 5)(x^2 - 3x + 5) = m^2 - n^2,$ then $m =$
  • ✓
    $x^2 + 5$
  • B
    $x^2 - 3x$
  • C
    $3x$
  • D
    None.
Answer
Correct option: A.
$x^2 + 5$
A.  $x^2 + 5$
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MCQ 291 Mark
Tick $(\checkmark)$ the correct answer:
$2x^2 + 5x + 3 = \ ?$
  • A
    $(x + 3)(2x + 1)$
  • ✓
    $(x + 1)(2x + 3)$
  • C
    $(2x + 5)(x − 3)$
  • D
    None of these
Answer
Correct option: B.
$(x + 1)(2x + 3)$
B.  $(x + 1)(2x + 3)$
Solution:
$2x^2+ 5x + 3$
$= 2x^2+ 2x + 3x + 3$
$= 2x(x + 1) + 3(x + 1)$
$= (2x + 3) (x + 1)$
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MCQ 301 Mark
Area of a quadrilateral $ABCD$ is $20cm^2$ and perpendiculars on $BD$ from opposite vertices are $1cm$ and $1.5cm.$ The length of $BD$ is:
  • A
    $4cm$
  • B
    $15cm$
  • ✓
    $16cm$
  • D
    $18cm$
Answer
Correct option: C.
$16cm$
Area of the given quadrilateral $=\frac{1}2{}$ (sum of altitudes) × Corresponding diagonal
$\Rightarrow20=\frac{1}{2}(1+1.5)\times\text{BD}$ [given]
$\Rightarrow\frac{1}2{}\times2.5\times\text{BD}=20\text{cm}^2$
$\Rightarrow\text{BD}=20\times\frac{2}{2.5}=\frac{40}{2.5}=16\text{cm}$
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MCQ 311 Mark
One of the factors of $a^3(b - c)^3+ b^3(c - a)^3+ c^3(a - b)$ is:
  • ✓
    $c - a$
  • B
    $b - c$
  • C
    $a - c$
  • D
    All the above.
Answer
Correct option: A.
$c - a$
A.  All the above.
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MCQ 321 Mark
The value of $0.645 \times 0.645 + 2 × 0.645 \times 0.355 + 0.355 \times 0.355$ is:
  • ✓
    $1$
  • B
    $0$
  • C
    $-1$
  • D
    $2$
Answer
Correct option: A.
$1$
A.  $1$
Solution:
Value $= (0.645 + 0.355)^2 = (1)^2 = 1$
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MCQ 331 Mark
Divide $96pqr(3p - 12) (5q - 30)$ by $144(p - 4) (q - 6)$
  • A
    $5pqr$
  • B
    $pqr$
  • C
    $\frac{2}{3}\text{pqr}$
  • ✓
    $10pqr$
Answer
Correct option: D.
$10pqr$

The division is expressed as a fraction
$\frac{96\text{pqr}(3\text{p}-12)(5\text{q}-30)}{144(\text{p}-4)(\text{q}-6)}$
$\Rightarrow\frac{12\times8\text{pqr}(3\text{p}-12)(5\text{q}-30)}{12\times12(\text{p}-4)(\text{q}-6)}$
$\Rightarrow\frac{12\times8\text{pqr}\times3(\text{p}-4)\times5(\text{q}-6)}{12\times12(\text{p}-4)(\text{q}-6)}$
$\Rightarrow\frac{8\text{pqr}\times3\times5}{12}$
$\Rightarrow\frac{4\times2\text{pqr}\times3\times5}{4\times3}$
Cancel the common factors in the numerator and denominator and solve
$\Rightarrow10\text{pqr}$

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MCQ 341 Mark
When we factorise an expression, we write it as a $...........$ of factors.
  • ✓
    Product
  • B
    Difference
  • C
    Sum
  • D
    None of these
Answer
Correct option: A.
Product
Product
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MCQ 351 Mark
Tick $(\checkmark)$ the correct answer:
$x^3 - x =\  ?$
  • A
    $x(x^2 - x)$
  • B
    $x(x - x^2)$
  • C
    $x(1 + x)(1 - x)$
  • ✓
    $x(x + 1)(x - 1)$
Answer
Correct option: D.
$x(x + 1)(x - 1)$
D.  $x(x + 1)(x - 1)$
Solution:
$x^3- x$
$= x(x^2- 1)$
$= x(x - 1)(x + 1)$
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MCQ 361 Mark
Factorize $12ab(9a^2 - 16b^2) \div 3ab(3a + 3b)$
  • A
    $(3a - 4b)$
  • B
    $(3a + 3b)$
  • C
    $(3a + 4b)$
  • ✓
    $(3a - 4b)$
Answer
Correct option: D.
$(3a - 4b)$
D.  $(3a - 4b)$
Solution:
Express the division as a fraction
$\frac{12\text{ab}(9\text{a}^2-16\text{b}^2)}{3\text{ab}(3\text{a}+4\text{b})}$
$\Rightarrow\frac{12\text{ab}((3\text{a})^3-(4\text{b}^2))}{3\text{ab}(3\text{a}+4\text{b})}$
$\Rightarrow\frac{12\text{ab}(3\text{a}+4\text{b})(3\text{a}-4\text{b})}{3\text{ab}(3\text{a}+4\text{b})}$
$\Rightarrow\frac{3\times4\text{ab}(3\text{a}+4\text{b})(3\text{a}-4\text{b})}{3\text{ab}(3\text{a}+4\text{b})}$
Cancel the common factors in the numerator and denominator
$\Rightarrow4(3\text{a}-4\text{b})$
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MCQ 371 Mark
The factors of $15x^2 - 26x + 8$ are:
  • A
    $(3x + 4)(5x + 2)$
  • B
    $(2x - 4)(5x + 2)$
  • C
    $(3x + 4)(5x - 2)$
  • ✓
    $(3x - 4)(5x - 2)$
Answer
Correct option: D.
$(3x - 4)(5x - 2)$
D.  $(3x - 4)(5x - 2)$
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MCQ 381 Mark
Which of the following is equal to $x^3 – 225x.$
  • A
    $x(1 - 15x) (1 + 15x)$
  • ✓
    $x(x - 15) (x + 15)$
  • C
    $x(1 - 15x) (1 - 15x)$
  • D
    $x(1 + 15x) (1 - 15x)$
Answer
Correct option: B.
$x(x - 15) (x + 15)$
B.  $x(x - 15) (x + 15)$
Solution:
Given, $x^3 - 225x$
By taking common $x,$
$\Rightarrow x(x^2 - 225)$
$\Rightarrow x(x^2 - 15^2)$
Now, using formula for $(a^2 - b^2)$
$\Rightarrow x(x - 15) (x + 15)$
As we know that $(a^2 - b^2) = (a + b) (a - b)$
Hence, $x^2 - 225x$ is equal to $x(x - 15) (x + 15).$
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MCQ 391 Mark
The factorisation of $z^2 - 4z - 12$ is:
  • A
    $(z + 6) (z + 2)$
  • B
    $(z - 6) (z - 2)$
  • ✓
    $(z - 6) (z + 2)$
  • D
    $(z + 6) (z - 2)$
Answer
Correct option: C.
$(z - 6) (z + 2)$
C.  $(z - 6) (z + 2)$
Solution:
$= z^3 - 4z – 12$
$= z^2 - 6z + 2z - 12$
$= z(z - 6) + 2(z - 6)$
$= (z - 6) (z + 2)$
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MCQ 401 Mark
The common factor of $10ab, 30bc, 50ca$ is:
  • ✓
    $10$
  • B
    $30$
  • C
    $50$
  • D
    $abc$
Answer
Correct option: A.
$10$

$10ab = 2 \times 5 \times a \times b$
$30bc = 2 \times 3 \times 5 \times b \times c$
$50ca = 2 \times 5 \times 5 \times c \times a$

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MCQ 411 Mark
The factorisation of $12a^2b + 15ab^2$ gives:
  • A
    $3ab(4ab + 5)$
  • ✓
    $3ab(4a + 5b)$
  • C
    $3a(4a + 5b)$
  • D
    $3b(4a + 5b)$
Answer
Correct option: B.
$3ab(4a + 5b)$
B.  $3ab(4a + 5b)$
Solution:
$12 a^2 b+15 a b^2 $
$12 a^2 b=3 \times 4 \times a \times a \times b $
$15 a b^2=3 \times 5 \times a \times b \times b$
The common factors are 3ab.
$12 a^2 b+15 a b^2=3 a b(4 a+5 b)$
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MCQ 421 Mark
The factors of $m^2 - 256$ are:
  • A
    $(m + 4)^2$
  • B
    $(m - 4)^2$
  • C
    $(m - 4) (m + 4)$
  • ✓
    None of the above.
Answer
Correct option: D.
None of the above.
D.  None of the above.
Solution:
$m^2 = (m)^2$ and $256 = (16)^2$
By using the algebraic identity,
$a^2 - b^2 = (a + b) (a - b),$
we get $(m + 16) (m - 16).$
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MCQ 431 Mark
What are the factors of $x^2 + xy - 2xz - 2yz?$
  • A
    $(x - y)$ and $(x + 2z)$
  • ✓
    $(x + y)$ and $(x - 2z)$
  • C
    $(x - y)$ and $(x - 2z)$
  • D
    $(x + y)$ and $(x + 2z)$
Answer
Correct option: B.
$(x + y)$ and $(x - 2z)$
B.  $(x + y)$ and $(x - 2z)$
View full question & answer→
MCQ 441 Mark
One of the factor of $a^3 + 8b^3 - 64c^3 + 24$ abc is:
  • A
    $a - 2b + 4c$
  • B
    $a + 2b + 4c$
  • ✓
    $a + 2b - 4c$
  • D
    $a - 2b - 4c$
Answer
Correct option: C.
$a + 2b - 4c$
C.  $a + 2b - 4c$
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MCQ 451 Mark
$39x^3 (50x^2 - 98) \div 26x^2 (5x + 7)$
  • A
    $3x(5x + 7)$
  • B
    $3x$
  • C
    $5x - 7$
  • ✓
    $3x(5x - 7)$
Answer
Correct option: D.
$3x(5x - 7)$
D.  $3x(5x - 7)$
Solution:
$\frac{39\text{x}^3(50\text{x}^2-98)}{26\text{x}^2(5\text{x}+7)}$
$\Rightarrow\frac{13\times3\text{x}^3\times2(25\text{x}^2-49)}{13\times2\text{x}^2(5\text{x}+7)}$
$\Rightarrow\frac{13\times3\text{x}^2\times2((5\text{x})^2-(7)^2)}{13\times2\text{x}^2\times(5\text{x}+7)}$
$\Rightarrow\frac{13\times3\text{x}^2\times2(5\text{x}+7)(5\text{x}-7)}{2\times13\text{x}^2(5\text{x}+7)}$
Cancel the common factors
$\Rightarrow3\text{x}(5\text{x}-7)$
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MCQ 461 Mark
One of the factors of $\text{x}^2 + \frac{1}{\text{x}^2} + 2 - 2\text{x} - \frac{2}{\text{x}}$ is:
  • A
    $\text{x}-\frac{1}{\text{x}}$
  • ✓
    $\text{x}+\frac{1}{\text{x}}$
  • C
    $\text{x}+\frac{1}{\text{x}}-1$
  • D
    None of these.
Answer
Correct option: B.
$\text{x}+\frac{1}{\text{x}}$
$\text{x}+\frac{1}{\text{x}}$
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MCQ 471 Mark
The factors of $\sqrt{3\text{x}^2} + 11\text{x} + 6\sqrt{3}$ are:
  • ✓
    $(\text{x} -3\sqrt{3})(\sqrt{3\text{x}} + 2)$
  • B
    $ac - bd + bc - ad$
  • C
    $(\text{x} + 3\sqrt{3}) (\sqrt{3\text{x}} + 2)$
  • D
    None of these.
Answer
Correct option: A.
$(\text{x} -3\sqrt{3})(\sqrt{3\text{x}} + 2)$
$(\text{x} -3\sqrt{3})(\sqrt{3\text{x}} + 2)$
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MCQ 481 Mark
What is the value of $(a + 4) (a + 2)$
  • A
    $a^2 + 6$
  • B
    $a^2 + 8$
  • ✓
    $a^2 + 6a + 8$
  • D
    $a^2 + 6a + 6$
Answer
Correct option: C.
$a^2 + 6a + 8$
C.  $a^2 + 6a + 8$
Solution:
$(a+4)(a+2) $
$ \Rightarrow a(a+2)+4(a+2) $
$ \Rightarrow a^2+2 a+4 a+8 $
$ \Rightarrow a^2+6 a+8$
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MCQ 491 Mark
Factorise: $p^4 - 81$
  • ✓
    $(p - 3) (p + 3) (p^2 + 9)$
  • B
    $(p + 3) (p^2 + 9)$
  • C
    $(p - 3) (p + 3)$
  • D
    None of these
Answer
Correct option: A.
$(p - 3) (p + 3) (p^2 + 9)$
A.   $(p - 3) (p + 3) (p^2 + 9)$
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MCQ 501 Mark
The factorisation of $12x + 36$ is:
  • A
    $12(x + 3)$
  • ✓
    $12(3x)$
  • C
    $12(3x + 1)$
  • D
    $x(12 + 36x)$
Answer
Correct option: B.
$12(3x)$

$= 12x + 36$
$= 12 x + 12.3$
$= 12(x + 3)$

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MCQ 511 Mark
The factorisation of $\text{x}^2+\text{x}+\frac{1}{4}$ is:
  • A
    $(\frac{\text{x}}{2}-1)^2$
  • B
    $(\frac{\text{x}}{2}+1)^2$
  • ✓
    $(\text{x}+\frac{1}{2})^2$
  • D
    $(\text{x}-\frac{1}{2})^2$
Answer
Correct option: C.
$(\text{x}+\frac{1}{2})^2$
$\text{x}^2+\text{x}+\frac{1}{4}$
$=\text{x}^2+2(\text{x})(\frac{1}{2})+(\frac{1}{2})^2$
$=(\text{x}+\frac{1}{2})^2$
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MCQ 521 Mark
The factorisation of $36x^2y^2 - 1$ is:
  • ✓
    $(6xy - 1) (6xy + 1)$
  • B
    $(6xy - 1)^2$
  • C
    $(6xy + 1)^2$
  • D
    $(6 + xy)^2$
Answer
Correct option: A.
$(6xy - 1) (6xy + 1)$
A.  $(6xy - 1) (6xy + 1)$
Solution:
$= 36x^2y^2 - 1 = (6xy)^2 - (1)^2$
$= (6xy - 1) (6xy + 1)$
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MCQ 531 Mark
The common factor of $6a^3b^4c^2, 21a^2b$ and $15a^3$ is:
  • ✓
    $3a^2$
  • B
    $3a^3$
  • C
    $6a^3$
  • D
    $6a^2$
Answer
Correct option: A.
$3a^2$
A.  $3a^2$
Solution:
$6 a^3 b^4 c^2=2 \times 3 \times a \times a \times a \times b \times b \times b \times b \times c \times c $
$ 21 a^2 b=3 \times 7 \times a \times a \times a $
$ 15 a^3 64 c 4=3 \times 5 \times a \times a \times a$
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MCQ 541 Mark
If $(\text{x}-\frac{1}{\text{x}})^2=\text{x}^2+\text{a}+\frac{1}{\text{x}^2}$ then a =
  • ✓
    $-2$
  • B
    $2$
  • C
    $2x$
  • D
    $-2x$
Answer
Correct option: A.
$-2$

$(\text{x}-\frac{1}{\text{x}})^2=\text{x}^2-2+\frac{1}{\text{x}^2}$
$\therefore\text{a}=-2$

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MCQ 551 Mark
Tick $(\checkmark)$ the correct answer:
$(2x - 32x^3) = ?$
  • A
    $2(x - 4)(x + 4)$
  • B
    $2x(1 - 2x)^2$
  • C
    $2x(1 + 2x)^2$
  • ✓
    $2x(1 - 4x)(1 + 4x)$
Answer
Correct option: D.
$2x(1 - 4x)(1 + 4x)$
D.  $2x(1 - 4x)(1 + 4x)$
Solution:
$2x - 32x^3 = 2x(1 - 16x^2)$
$= 2x{(1)^2 - (4x)^2}$
$= 2x(1 - 4x)(1 + 4x)$
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MCQ 561 Mark
The factorisation of $4y^2 - 12y + 9$ is:
  • A
    $(2y + 3)^2$
  • ✓
    $(2y - 3)^2$
  • C
    $(3y + 2)^2$
  • D
    $(3y - 2)^2$
Answer
Correct option: B.
$(2y - 3)^2$
B.  $(2y - 3)^2$
Solution:
$= 4y^2 - 12y + 9$
$= (2y)^2 - 2(2y)(3) + (3)^2$
$= (2y - 3)^2$
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MCQ 571 Mark
Which of the following is one of the factors of $x^4 + 4\ ?$
  • A
    $x^2+2$
  • ✓
    $(x^2 + 2 + 2x)(x^2 + 2 - 2x)$
  • C
    $x^2 - 2$
  • D
    $x^2 + 2x - 2$
Answer
Correct option: B.
$(x^2 + 2 + 2x)(x^2 + 2 - 2x)$
B.  $(x^2 + 2 + 2x)(x^2 + 2 - 2x)$
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MCQ 581 Mark
The factorisation of $10x^2 - 18x^3 + 14x^4$ is:
  • ✓
    $2x^2 (7x^2 - 9x + 5)$
  • B
    $2x (7x^2 - 9x + 5)$
  • C
    $2\  (7x^2 - 9x + 5)$
  • D
    $2x^3\  (7x^2 - 9x + 5)$
Answer
Correct option: A.
$2x^2 (7x^2 - 9x + 5)$
A.  $2x^2 (7x^2 - 9x + 5)$
Solution:
$10x^2 - 18x^2 + 14x^2 = 2x^2(5 - 9x + 7x^2)$
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MCQ 591 Mark
The factorisation of $am^2 + bm^2 + bn^2 + an^2$ is:
  • A
    $(a + b) (m^2 - n^2)$
  • ✓
    $(a + b) (m^2 + n^2)$
  • C
    $(a - b) (m^2 + n^2)$
  • D
    $(a - b) (m^2 - n^2)$
Answer
Correct option: B.
$(a + b) (m^2 + n^2)$
B.  $(a + b) (m^2 + n^2)$
Solution:
$= am^2 + bm^2 + bn^2 + an^2$
$= m^2(a + b) + n^2(b + a)$
$= (a + b) (m^2 + n^2)$
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MCQ 601 Mark
The value of $(0.68)^2 - (0.32)^2$ is:
  • A
    $-1$
  • B
    $0$
  • C
    $1$
  • ✓
    $0.36$
Answer
Correct option: D.
$0.36$
D.  $0.36.$
Solution:
Value $= (0.68 + 0.32) (0.68 - 0.32) = 0.36.$
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MCQ 611 Mark
Nia has solved $(x + 4)^2 = x^2 + 16$ correct if required.
  • A
    $(x + 4)^2 = x^2 + 8 - 8x$
  • ✓
    $(x + 4)^2 = x^2 + 16 + 8x$
  • C
    $(x + 4)^2 = x^2 + 8$
  • D
    $(x + 4)^2 =x^2 -16$
Answer
Correct option: B.
$(x + 4)^2 = x^2 + 16 + 8x$
B.  $(x + 4)^2 = x^2 + 16 + 8x$
Solution:
Expand $(x + 4)^2$ using the indentity, $(a + b)^2 = a^2 + b^2 + 2ab$
$\Rightarrow (x + 4)^2 = x^2 + 4^2 + 2 × x × 4 = x^2 +16 + 8x$
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MCQ 621 Mark
The factorisation of $x^2 - 9$ is:
  • A
    $(x – 3)^2$
  • B
    $(x + 3)^2$
  • ✓
    $(x + 3) (x – 3)$
  • D
    None of these.
Answer
Correct option: C.
$(x + 3) (x – 3)$
C.  $(x + 3) (x - 3)$
Solution:
$x^2 - 9 = (x)^2 - (3)^2 $
$= (x - 3) (x + 3)$
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MCQ 631 Mark
If the factors of $a^2 + b^2 + 2(ab + bc + ca)$ are $(a + b + m)$ and $(a + b + nc),$ then the value of $m + n$ is:
  • A
    $6$
  • B
    $4$
  • C
    $0$
  • ✓
    $2$
Answer
Correct option: D.
$2$
D.  $2$
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MCQ 641 Mark
The factorisation of $6x^2 - 5x - 6$ is:
  • ✓
    $(2x - 3) (3x + 2)$
  • B
    $(2x + 3) (3x + 2)$
  • C
    $(2x - 3) (3x - 2)$
  • D
    $(2x + 3) (3x - 2)$
Answer
Correct option: A.
$(2x - 3) (3x + 2)$
A.  $(2x - 3) (3x + 2)$
Solution:
$= 6x^2 - 5x - 6$
$= 6x^2 - 9x + 4x - 6$
$= 3x(2x - 3) + 2(2x - 3)$
$= (2x – 3) (3x + 2)$
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MCQ 651 Mark
Tick $(\checkmark)$ the correct answer:
$ab - mn + an - bm = ?$
  • A
    $(a - b)(m - n)$
  • ✓
    $(a - m)(b + n)$
  • C
    $(a - n)(m + b)$
  • D
    $(m - a)(n - b)$
Answer
Correct option: B.
$(a - m)(b + n)$

$ab - mn + an - bm$
$= ab + an - bm - mn$
$= a(b + n) - m(b + n)$
$= (a - m)(b + n)$

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MCQ 661 Mark
The value of $\frac{0.564\times0.564\times-0.436\times0.436}{0.564-0.436}$ is:
  • A
    $0$
  • ✓
    $1$
  • C
    $-1$
  • D
    None of these
Answer
Correct option: B.
$1$

Value $=\frac{(0.564+0.436)(0.564-0.436)}{0.564-0.436}=1$

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MCQ 671 Mark
The factors of $4y^2 - 12y + 9$ is:
  • A
    $(2y + 3)^2$
  • ✓
    $(2y - 3)^2$
  • C
    $(2y - 3) (2y + 3)$
  • D
    None of the above.
Answer
Correct option: B.
$(2y - 3)^2$
B.  $(2y - 3)^2$
Solution:
$=4 y^2-12 y+9 $
$ =4 y^2=(2 y)^2 \& 9=3^2 \& 12 y=2.3 .2 y $
$ =4 y^2-12 y+9=(2 y)^2-2 \times 3 \times(2 y)+(3)^2 $
$ =(2 y-3)^2 \text { By algebraic identities: }(a-b)^2=a^2+b^2-2 a b$
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MCQ 681 Mark
Tick $(\checkmark)$ the correct answer:
$x^2 + 4x - 21 = ?$
  • A
    $(x - 7)(x + 3)$
  • ✓
    $(x + 7)(x - 3)$
  • C
    $(x - 7)(x - 3)$
  • D
    $(x + 7)(x + 3)$
Answer
Correct option: B.
$(x + 7)(x - 3)$
B.  $(x + 7)(x - 3)$
Solution:
$x^2 + 4x - 21$
$= x^2+ 7x - 3x - 21$
$= x(x + 7) - 2(x + 7)$
$= (x - 3)(x + 7)$
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MCQ 691 Mark
What is the coefficient of $'a'$ when $9a^2 + 18a$ is divided by $(a + 2)\ ?$
  • A
    $18$
  • ✓
    $9$
  • C
    $\frac{1}{2}$
  • D
    $2$
Answer
Correct option: B.
$9$
B.  $9$
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MCQ 701 Mark
The quotient of $28x^2 + 14x$ is:
  • A
    $2$
  • ✓
    $2x$
  • C
    $x$
  • D
    $x^2$
Answer
Correct option: B.
$2x$
B.  $2x$
Solution:
$\frac{28\text{x}^21}{14\text{x}}=\frac{2\times2\times7\times\text{x}\times\text{x}}{2\times7\times\text{x}}=2\text{x}$
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MCQ 711 Mark
The factorisation of $6x - 42$ is:
  • ✓
    $6(x - 7)$
  • B
    $3(x - 7)$
  • C
    $2(x - 7)$
  • D
    $6(x + 7)$
Answer
Correct option: A.
$6(x - 7)$
$6x – 42 = 6(x - 7)$
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MCQ 721 Mark
The factorisation of $x^2yz + xy^2z + xyz^2$ is:
  • ✓
    $xyz(x + y + z)$
  • B
    $x^2yz(x + y + z)$
  • C
    $xy^2z(x + y + z)$
  • D
    $xyz^2(x + y + z)$
Answer
Correct option: A.
$xyz(x + y + z)$
A.  $xyz(x + y + z)$
Solution:
$x^2yz + xy^2z + xyz^2 = xyz (x + y + z)$
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MCQ 731 Mark
The common factor of $24x^3y^4, 36x^4z^4$ and $48x^3y^2z$ is:
  • ✓
    $12x^3$
  • B
    $24x^3$
  • C
    $36x^3$
  • D
    $48x^3$
Answer
Correct option: A.
$12x^3$
A.  $12x^3$
Solution:
$24x^3y^4 = 2 \times 2 \times 2 \times 3 \times x \times x \times x \times y \times y \times y \times y$
$36x^4z^4 = 2 \times 2 \times 3 \times 3 \times x \times x \times x \times x \times z \times z \times z \times z$
$48x^3y^2z = 2 \times 2 \times 2 \times 2 \times 3 \times x \times x \times x \times y \times y \times z$
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MCQ 741 Mark
The common factor of $a^3b^3$ and $ab^2$ is:
  • A
    $a^2b^2$
  • B
    $a^2b$
  • C
    $ab$
  • ✓
    $ab^2$
Answer
Correct option: D.
$ab^2$
D.  $ab^2$
Solution:
$a^3b^3 = a \times a \times a \times b \times b \times b$
$ab^2 = a \times b \times b$
The common factors are:$ a \times b \times b = ab^2$
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MCQ 751 Mark
The factorisation of $(\frac{{\text{x}^2}}{{\text{y}}^2}-2+\frac{{\text{y}^2}}{{\text{x}^2}})\text{x}\not=0$ is:
  • A
    $(\frac{\text{x}}{\text{y}}+\frac{\text{y}}{\text{x}})^2$
  • ✓
    $(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
  • C
    $(\frac{\text{x}}{\text{y}}-1)^2$
  • D
    $(\frac{\text{x}}{\text{y}}+1)^2$
Answer
Correct option: B.
$(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
$=\frac{​​\text{x}^2}{\text{y}^2}-2+\frac{\text{y}^2}{\text{x}^2}$
$=(\frac{\text{x}}{\text{y}})^2-2(\frac{\text{x}}{\text{y}})(\frac{\text{y}}{\text{x}})+(\frac{\text{y}}{\text{x}})^2$
$=(\frac{\text{x}}{\text{y}}-\frac{\text{y}}{\text{x}})^2$
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MCQ 761 Mark
Tick $(\checkmark)$ the correct answer:
$4z^2 - 8z + 3 = \ ?$
  • ✓
    $(2z - 1)(2z - 3)$
  • B
    $(2z + 1)(3 - 2z)$
  • C
    $(2z + 3)(3z - 1)$
  • D
    $(z - 1)(4z - 3)$
Answer
Correct option: A.
$(2z - 1)(2z - 3)$
A.  $(2z - 1)(2z - 3)$
Solution:
$4 z^2-8 z+3 $
$ =4 z^2-6 z-2 z+3 $
$ \{4 \times 3=12,12=(-6) \times(-2),-8=-6-2\} $
$ =2 z(2 z-3)-1(2 z-3) $
$ =(2 z-1)(2 z-3)$
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MCQ 771 Mark
Divide as directed: $5 (2x + 1) (3x + 5) ÷ (2x + 1)$
  • A
    $(3x + 5)$
  • B
    $5$
  • ✓
    $5 (3x + 5)$
  • D
    None of these.
Answer
Correct option: C.
$5 (3x + 5)$
$5 (3x + 5)$
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MCQ 781 Mark
The quotient of $12a^8b^8 + (-a^6b^6)$ is:
  • A
    $3a^2b^2$
  • B
    $3a^2b$
  • C
    $3ab^2$
  • ✓
    $-3a^2b^2$
Answer
Correct option: D.
$-3a^2b^2$
D.  $-3a^2b^2$
Solution:
$=-\frac{12\text{a}^8\text{b}^8}{4\text{a}^6\text{b}^8}$
$=-\frac{2\times2\times3\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}}{2\times2\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{a}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}\times\text{b}}$
$=-3\text{a}^2\text{b}^2$
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MCQ 791 Mark
Tick $(\checkmark)$ the correct answer:
$(12m^2 - 27) =\  ?$
  • A
    $(2m - 3)(3m - 9)$
  • B
    $3(2m - 9)(3m - 1)$
  • ✓
    $3(2m - 3)(2m + 3)$
  • D
    None of these
Answer
Correct option: C.
$3(2m - 3)(2m + 3)$
c.  $3(2m - 3)(2m + 3)$
Solution:
$12m^2- 27$
$= 3(4m^2- 9)$
$= 3(2m - 3)(2m + 3)$
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MCQ 801 Mark
The factors of $x^2 + 2x^2 + 9$ is:
  • A
    $(x^2 + 3)(x^2 - 3)$
  • ✓
    $(x^2 - 2x +3)(x^2 + 2x +3)$
  • C
    Factorization is not possible.
  • D
    None of these.
Answer
Correct option: B.
$(x^2 - 2x +3)(x^2 + 2x +3)$
B.  $(x^2 - 2x +3)(x^2 + 2x +3)$
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MCQ 811 Mark
Which of the following is quotient obtained on dividing $-18xyz^2$ by $-3xz?$
  • ✓
    $6yz$
  • B
    $-6yz$
  • C
    $6xy^2$
  • D
    $6xy$
Answer
Correct option: A.
$6yz$
A.  $6yz$
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MCQ 821 Mark
Correct the error in $(2x)^2 + 5(2x) + 7 = 2x^2 + 7x + 7$
  • A
    $(2x)^2 + 5(2x) + 7 = 4x + 7x + 7$
  • ✓
    $(2x)^2 + 5(2x) + 7 = 4x^2 + 10x + 7$
  • C
    $(2x)^2 + 5(2x) + 7 = 4x^2 + 7x + 7$
  • D
    $(2x)^2 + 5(2x) + 7 = 4x + 10x + 7$
Answer
Correct option: B.
$(2x)^2 + 5(2x) + 7 = 4x^2 + 10x + 7$
B.  $(2x)^2 + 5(2x) + 7 = 4x^2 + 10x + 7$
Solution:
Consider the Left Hand Side of the given equation,
$(2x)^2 + 5(2x) + 7$
$\Rightarrow (2x \times 2x) + 5 \times (2x) + 7$
$\Rightarrow 4x^2 +10x +7$
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MCQ 831 Mark
Divide as directed: $26xy (x + 5) (y - 4) ÷ 13x (y - 4)$
  • ✓
    $2y(x + 5)$
  • B
    $(x + 5)$
  • C
    $2y$
  • D
    None of these
Answer
Correct option: A.
$2y(x + 5)$
$2y(x + 5)$
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MCQ 841 Mark
Tick $(\checkmark)$ the correct answer:
$x^2 + 6x + 8 = ?$
  • A
    $(x + 3)(x + 5)$
  • B
    $(x + 3)(x + 4)$
  • ✓
    $(x + 2)(x + 4)$
  • D
    $(x + 1)(x + 8)$
Answer
Correct option: C.
$(x + 2)(x + 4)$
C.  $(x + 2)(x + 4)$
Solution:
$x^2 + 6x + 8$
$= x^2+ 4x + 2x + 8$
${8 = 4 × 2, 6 = 4 + 2}$
$= x(x + 4) + 2(x + 4)$
$= (x + 2)(x + 4)$
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MCQ 851 Mark
The factors of $x^2 + xy + 8x + 8y$ are:
  • A
    $(2x + y) (x + 8)$
  • B
    $(x + 2y) (x + 8)$
  • ✓
    $(x + y) (x + 8)$
  • D
    $(x + y) (2x + 8)$
Answer
Correct option: C.
$(x + y) (x + 8)$
C.  $(x + y) (x + 8)$
Solution:
$= x^2 + xy + 8x + 8y$
$= x(x + y) + 8(x + y)$
$=(x + y) (x + 8)$
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MCQ 861 Mark
The factorisation of $6xy - 4y + 6 - 9x$ is:
  • ✓
    $(3x - 2)(2y - 3)$
  • B
    $(3x + 2)(2y - 3)$
  • C
    $(3x - 2)(2y + 3)$
  • D
    $(3x + 2)(2y + 3)$
Answer
Correct option: A.
$(3x - 2)(2y - 3)$

$= 6xy - 4y + 6 - 9x$
$= 2y(3x - 2) - 3(- 2 + 3x)$
$= (3x - 2)(2y - 3)$

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MCQ 871 Mark
Tick $(\checkmark)$ the correct answer:
$ab - a - b + 1 = ?$
  • ✓
    $(a - 1)(b - 1)$
  • B
    $(1 - a)(1 - b)$
  • C
    $(a - 1)(1 - b)$
  • D
    $(1 - a)(b - 1)$
Answer
Correct option: A.
$(a - 1)(b - 1)$

$ab - a - b + 1$
$= a(b - 1) - 1(b - 1)$
$= (a - 1)(b - 1)$

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MCQ 881 Mark
When we factorise $x^2 + 5x + 6,$ then we get:
  • A
    $(x - 2) (x - 3)$
  • B
    $(x \times 2) + (x \times 3)$
  • ✓
    $(x + 2) (x + 3)$
  • D
    $(x \times 2) - (x \times 3)$
Answer
Correct option: C.
$(x + 2) (x + 3)$
C.  $(x + 2) (x + 3)$
Solution:
The factors of a form:
$= (x + a) (x + b) = x^2 + (a + b) x + ab$
$= x^2 + 5x + 6$
$= a + b = 5$ and $ab = 6$
$= x^2 + 5x + 6 = (x + 2) (x + 3)$
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MCQ 891 Mark
The common factor of $2x, 3x^3, 4$ is:
  • ✓
    $1$
  • B
    $2$
  • C
    $3$
  • D
    $4$
Answer
Correct option: A.
$1$
A.  $1$
Solution:
$3x^3 = 3 \times x \times x \times x$
$4 = 2 \times 2$
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MCQ 901 Mark
The common factor $12y$ and $30$ is:
  • ✓
    $6$
  • B
    $12$
  • C
    $30$
  • D
    $6y$
Answer
Correct option: A.
$6$
$12y = 2 \times 2 \times 3 \times y$
$30 = 2 \times 3 \times 5$
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MCQ 911 Mark
The factorisation of $12a^2b + 15ab^2$ is:
  • ✓
    $3ab (4a + 5b)$
  • B
    $3a^2b (4a + 5b)$
  • C
    $3ab^2 (4a + 5b)$
  • D
    $3a^2b^2 (4a + 5b)$
Answer
Correct option: A.
$3ab (4a + 5b)$
A.  $3ab (4a + 5b)$
Solution:
$12a^2b + 15ab^2 = 3ab(4a + 5b)$
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MCQ 921 Mark
The factorisation of $x^2 + x + xy + y + zx + z$ is:
  • ✓
    $(x + y + z) (x + 1)$
  • B
    $(x + y + z) (x + y)$
  • C
    $(x + y + z) (y + z)$
  • D
    $(x + y + z) (z + x)$
Answer
Correct option: A.
$(x + y + z) (x + 1)$
A.  $(x + y + z) (x + 1)$
Solution:
$= x^2 + x + xy + y + zx + z$
$= x(x + 1) + y(x + 1) + z(x + 1)$
$= (x + 1) (x + y + z)$
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MCQ 931 Mark
Factorize by grouping $15pq + 15 + 9q +25p$
  • A
    $(pq + 1) (3q + 5p)$
  • B
    $(3pq + 5p) (5 + 3q)$
  • C
    $(3q + 3) (5p + 5)$
  • ✓
    $(3q + 5) (5p + 3)$
Answer
Correct option: D.
$(3q + 5) (5p + 3)$
To factorize this expression, rearrange the terms in tills expression $= 15pq +25p + 9q + 15$
Take Sp as the common factor of the first two terms and $3$ as the common factor of the other two terms.
$= 5p(3q + 5) + 3(3q + 5)$
$= (3q + 5) (5p + 3)$
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MCQ 941 Mark
The value of $0.76 \times 0.76 \times 0.76 + 0.24 \times 0.24 \times \frac{0.24}{0.76} \times 0.76 - 0.76 \times 0.24 + 0.24 + 0.24$ is:
  • ✓
    $1$
  • B
    $0.1$
  • C
    $0.52$
  • D
    $0.01$
Answer
Correct option: A.
$1$
$1$
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MCQ 951 Mark
The factors of $xyz$ are:
  • A
    $x$
  • B
    $y$
  • C
    $z$
  • ✓
    All of the above.
Answer
Correct option: D.
All of the above.

$x, y$ and $z$ are all the factors of $xyz.$

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MCQ 961 Mark
The factors of $4y^2- 12y + 9$ is:
  • ✓
    $(2y - 3)^2$
  • B
    $(2y + 3)^2$
  • C
    $(2y - 3) (2y + 3)$
  • D
    None of the above.
Answer
Correct option: A.
$(2y - 3)^2$
A.  $(2y - 3)^2$
Solution:
$= 4y^2- 12y + 9$
$= 4y^2 = (2y)^2 \&\  9 = 3^2 \&\  12y = 2.3.2y$
$= 4y^2- 12y + 9 = (2y)^2 - 2 \times 3 \times (2y) + (3)^2$
$= (2y - 3)^2$ By algebraic identities: $(a - b)^2 = a^2+b^2 - 2ab.$
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MCQ 981 Mark
The real factors of $x^2 + 4$ are:
  • A
    $(x + 2) (x - 2)$
  • B
    $(x^2 + 2) (x^2​​​​​​​ - 2)$
  • ✓
    Does not exist.
  • D
    None of these.
Answer
Correct option: C.
Does not exist.
C.  Does not exist.
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MCQ 991 Mark
The value of $99^2$ is:
  • A
    $(90)^2 + 2(90)(9) + (9)^2$
  • ✓
    $(90)^2 - 2(90)(9) + (9)^2$
  • C
    $(90)^2 + (9)^2$
  • D
    None of these.
Answer
Correct option: B.
$(90)^2 - 2(90)(9) + (9)^2$
B.  $(90)^2 + 2(90) (9) + (9)^2$
Solution:
$= 99^2 = (90 + 9)^2$
$= (90)^2 + 2(90) (9) + (9)^2$
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MCQ 1001 Mark
Tick $(\checkmark)$ the correct answer:
$40 + 3x - x^2 = ?$
  • A
    $(x + 5)(x - 8)$
  • B
    $(5 - x)(8 + x)$
  • ✓
    $(5 + x)(8 - x)$
  • D
    $(5 - x)(8 - x)$
Answer
Correct option: C.
$(5 + x)(8 - x)$
C.  $(5 + x)(8 - x)$
Solution:
$40 + 3x - x^2$
$= 40 + 8x - 5x - x^2$
${40 = 8x(-5), 3 = 8 - 5}$
$= 8(5 + x) - x(5 + x)$
$= (8 - x)(x + 5)$
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MCQ 1011 Mark
Which of the following are the factors of $a^2 - ab - ca + bc.$
  • A
    $(b + c) (c + a)$
  • ✓
    $(a - b) (a - c)$
  • C
    $a(a + b + c)$
  • D
    $(a + b) (b + c)$
Answer
Correct option: B.
$(a - b) (a - c)$
b.  $(a - b) (a - c)$
Solution:
$= a^2 - ab - ca + bc$
$= a(a - b) - c(a - b)$
$= (a - b) (a - c)$
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MCQ 1021 Mark
Which of the following is the factorisation of $x^3 - x\ ?$
  • A
    $x(x - x^2)$
  • B
    $x[(1+ x) (1 - x)]$
  • C
    $x(x^2 - x)$
  • ✓
    $x(x + 1) (x - 1)$
Answer
Correct option: D.
$x(x + 1) (x - 1)$
d.  $x[(x + 1) (x - 1)]$
Solution:
$x^3 - x$
Take x as common
$x(x^2 - 1)$
Property: $x^2 - a^2 = (x - a) (x + a)$
Applying the property
$x(x - 1) (x + 1)$
So, Factorization of $x^3 - x$ is $x(x - 1) (x + 1)$
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MCQ 1031 Mark
The value of $49^2$ is:
  • ✓
    $(50)^2 - 2(50) (1) + (1)^2$
  • B
    $(50)^2 + 2 (50) (1) + (1)^2$
  • C
    $(50)^2 - (1)^2$
  • D
    $(50)^2 + (1)^2$
Answer
Correct option: A.
$(50)^2 - 2(50) (1) + (1)^2$
A.  $(50)^2 - 2(50) (1) + (1)^2$
Solution:
$= 49^2 = (50 - 1)^2$
$= (50)^2 - 2(50) (1) + (1)^2$
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MCQ 1041 Mark
The factors of $6xy - 4y + 6 - 9x$ are:
  • A
    $(3x + 2) (2y + 3)$
  • B
    $(3x - 2) (2y - 3)$
  • C
    $(3x - 2) (2y + 3)$
  • ✓
    $(3x + 2) (2y - 3)$
Answer
Correct option: D.
$(3x + 2) (2y - 3)$

$= 6xy - 4y + 6 - 9x$
$= 6xy - 4y - 9x + 6$
$= 2y(3x - 2) - 3(3x - 2)$
$= (3x - 2) (2y - 3)$

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MCQ 1051 Mark
What is the value of $(3a + 4b) (a - b)$
  • A
    $3a^2 - ab - 4b^2$
  • ✓
    $3a^2 + ab - 4b^2$
  • C
    $(3a^2 + 4b^2)$
  • D
    $(3a^2 - 4b^2)$
Answer
Correct option: B.
$3a^2 + ab - 4b^2$
B.  $3a^2 + ab - 4b^2$
Solution:
$(3a + 4b) (a - b)$
$\Rightarrow 3a(a - b) + 4b (a - b)$
$\Rightarrow 3a^2 - 3ab + 4ab - 4b^2$
$\Rightarrow 3a^2 + ab - 4b^2$
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MCQ 1061 Mark
Which of the following is the common factor of $21x^2y$ and $35xy^2\ ?$
  • A
    $7$
  • B
    $xy$
  • ✓
    $7xy$
  • D
    None of these.
Answer
Correct option: C.
$7xy$
C.  $7xy$
Solution:
$21x^2y = 3 \times 7 \times x \times x \times y$
$35x,\  y^2 = 7 \times 5 \times x \times y \times y$
Thus, the common factors are common factors of $21x^2y$ and $35xy^2$ are $7, x, y.$
$(7 \times x \times y) = 7xy$
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MCQ 1071 Mark
Find the factors of $4p^4 + 12p + 8$
  • A
    $(p^2 + 3p + 2)$
  • B
    $4(p^2 + 3p + 2)$
  • C
    $(p + 1) (p + 2)$
  • ✓
    $4(p + 1) (p + 2)$
Answer
Correct option: D.
$4(p + 1) (p + 2)$
D.  $4(p + 1) (p + 2)$
Solution:
$4 p^4+12 p+8$
Take $4$ as the common factor
$\Rightarrow 4\left( p ^2+3 p +2\right)$
Split the middle term
$\Rightarrow 4\left(p^2+2 p+p+2\right) $
$\Rightarrow 4(p(p+2)+1(p+2)) $
$\Rightarrow 4(p+1)(p+2)$
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MCQ 1081 Mark
The factorisation of $ax^2y + bxy^2 + cxyz$ is:
  • ✓
    $xy(ax + by + cz)$
  • B
    $axy(ax + by + cz)$
  • C
    $bxy(ax + by + cz)$
  • D
    $cxy(ax + by + cz)$
Answer
Correct option: A.
$xy(ax + by + cz)$
A.  $xy(ax + by + cz)$
Solution:
$ax^2y + bxy^2 + cxyz = xy (ax + by + cz)$
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MCQ 1091 Mark
The common factor of $8a^2b^4c^2, 12a^4bc^4$ and $20a^3b^4$ is:
  • A
    $a^4b^4$
  • B
    $a^2b^2$
  • C
    $4a^2b^2$
  • ✓
    $4a^2b$
Answer
Correct option: D.
$4a^2b$
D.  $4a^2b.$
Solution:
$8 a^2 b^4 c^2=2 \times 2 \times 2 \times a \times a \times b \times b \times b \times b \times c \times c $
$ 12 a^4 b c^2=2 \times 2 \times 3 \times a \times a \times a \times a \times b \times c \times c $
$ 20 a^3 b^4=2 \times 2 \times 5 \times a \times a \times a \times b \times b \times b \times b$
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MCQ 1101 Mark
The factorisation of $12x + 36$ is.
  • A
    $12(3x)$
  • B
    $12(3x + 1)$
  • ✓
    $12(x + 3)$
  • D
    $x(12 + 36x)$
Answer
Correct option: C.
$12(x + 3)$

$= 12x + 36$
$= 12 x + 12.3$
$=12(x + 3)$

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MCQ 1111 Mark
Factorise: $x^4 - (x - z)4$
  • A
    $(2x^2 - 2xz + z^2)$
  • B
    $(2x - z) (2x^2 - 2xz + z^2)$
  • ✓
    $z(2x - z) (2x^2 - 2xz + z^2)$
  • D
    None of these
Answer
Correct option: C.
$z(2x - z) (2x^2 - 2xz + z^2)$
C.  $z(2x - z) (2x^2 - 2xz + z^2)$
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MCQ 1121 Mark
The common factor of $x^3y^2$ and $x^4y$ is:
  • A
    $x^4y^2$
  • B
    $x^4y$
  • C
    $x^3y^2$
  • ✓
    $x^3y$
Answer
Correct option: D.
$x^3y$
$x^3y^2 = x \times x \times x \times y \times y$
$x^4y = x \times x \times x \times x \times y$
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MCQ 1131 Mark
The common factor of $2a^2b^4c^2, 8a^4b^3c^4$ and $6a^3b^4c^2$ is:
  • ✓
    $2a^2b^3c^2$
  • B
    $6a^2b^3c^2$
  • C
    $8a^2b^3c^2$
  • D
    $a^4b^4c^4$
Answer
Correct option: A.
$2a^2b^3c^2$
A.  $2a^2b^3c^2$
Solution:
$6 a^2 b^4 c^2=2 \times a \times a \times b \times b \times b \times b \times c \times c \times c \times c $
$8 a^4 b^3 c^4=2 \times 2 \times 2 \times a \times a \times a \times a \times b \times b \times b \times c \times c \times c \times c $
$6 a^3 b^4 c^2=2 \times 3 \times a \times a \times a \times b \times b \times b \times b \times c \times c$
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MCQ 1141 Mark
If $x^2 - x - 42 = (x + k) (x + 6),$ then $k =$
  • A
    $6$
  • B
    $-6$
  • C
    $7$
  • ✓
    $-7$
Answer
Correct option: D.
$-7$
D.  $-7$
Solution:
$x^2 - x - 42$
$= x^2 - 7x + 6x - 42$
$= x(x - 7) + 6(x - 7)$
$= (x - 7) (x + 6)$ $\therefore$ $k = -7$
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MCQ 1151 Mark
The common factor of $6x^3y^4z^2, 21x^2y$ and $15x^3$ is:
  • A
    $3x^3$
  • B
    $6x^3$
  • ✓
    $3x^2$
  • D
    $6x^2$
Answer
Correct option: C.
$3x^2$
Same as question number $14.$
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MCQ 1161 Mark
Find and correct the errors in the following mathematical statements.
$x(3x + 2) = 3x^2 + 2$
  • ✓
    $x(3x + 2) = 3x^2 + 2x$
  • B
    $x(3x + 2) = 3x^2$
  • C
    $x(3x + 2) = 5x^2+ 2x$
  • D
    None of these
Answer
Correct option: A.
$x(3x + 2) = 3x^2 + 2x$
A.  $x(3x + 2) = 3x^2 + 2x$
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MCQ 1171 Mark
Divide as directed: $52pqr (p + q) (q + r) (r + p) ÷ 104pq (q + r) (r + p)$
  • A
    $r(p + q)$
  • ✓
    $\frac{1}{2} \text{r}(\text{p}+\text{q})$
  • C
    $\frac{1}{2}$
  • D
    None of these.
Answer
Correct option: B.
$\frac{1}{2} \text{r}(\text{p}+\text{q})$
$\frac{1}{2} \text{r}(\text{p}+\text{q})$
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MCQ 1181 Mark
The common factor of $p^3q^4$ and $p^4q^3$ is:
  • A
    $p^4q^4$
  • B
    $p^4q$
  • ✓
    $p^3q^3$
  • D
    $p^3q^4$
Answer
Correct option: C.
$p^3q^3$
C.  $p^3q^3$
Solution:
$p^3q^4 = p \times p \times p \times q \times q \times q \times q$
$p^4q^3 = p \times p \times p \times p \times q \times q \times q$
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MCQ 1191 Mark
One of the factors of $(a^2 - b^2)(c^2 - d^2) - 4abcd$ is:
  • A
    $ac - bd + bc - ad$
  • B
    $(ac - bd + bc + ad)$
  • ✓
    Cannot be determined.
  • D
    None of these.
Answer
Correct option: C.
Cannot be determined.
C.  Cannot be determined.
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MCQ 1201 Mark
Which of the following statements is correct?
  • ✓
    $(a - 4)(a - 2) = a^2 + 8 - 6a$
  • B
    $(2p + 3q)(p - q) = 2p^2 - 3q^2$
  • C
    $\frac{3\text{p}^2}{3\text{p}^2}=0$
  • D
    $4(m - 5) = 4m - 5$
Answer
Correct option: A.
$(a - 4)(a - 2) = a^2 + 8 - 6a$
A.  $(a - 4)(a - 2) = a^2 + 8 - 6a$
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MCQ 1211 Mark
Which of the following is a factor of $z^2 - 4z - 12?$
  • A
    $z + 6$
  • B
    $z - 6$
  • C
    $z^2 - 12$
  • ✓
    $z + 2$
Answer
Correct option: D.
$z + 2$
D.  $z + 2$
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MCQ 1221 Mark
Tick $(\checkmark)$ the correct answer:
$3 + 23y - 8y^2 = \ ?$
  • A
    $(1 - 8y)(3 + y)$
  • ✓
    $(1 + 8y)(3 - y)$
  • C
    $(1 - 8y)(y - 3)$
  • D
    $(8y - 1)(y + 3)$
Answer
Correct option: B.
$(1 + 8y)(3 - y)$
B.  $(1 + 8y)(3 - y)$
Solution:
$3+23 y-8 y^2 $
$=3+24 y-y-8 y^2 $
$ \{3 \times(-8)=-24,-24=24 \times(-1), 23=24-1\} $
$ =3(1+8 y)-y(1+8 y) $
​​​​​​​$ =(1+8 y)(3-y)$
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MCQ 1231 Mark
The factorisation of $ax + bx - ay - by$ is:
  • ✓
    $(x - y) (a + b)$
  • B
    $(x + y) (a + b)$
  • C
    $(x - y) (a - b)$
  • D
    $(x + y) (a - b)$
Answer
Correct option: A.
$(x - y) (a + b)$

$= ax + bx - ay - by$
$= x(a + b) - y(a + b)$
$= (x - y)(a + b)$

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MCQ 1241 Mark
The factorisation of $12x^2y + 15xy^2$ is:
  • A
    $3xy^2(4x + 5y)$
  • B
    $3x^2y(4x + 5y)$
  • C
    $3x^2y^2(4x + 5x)$
  • ✓
    $3xy(4x + 5y)$
Answer
Correct option: D.
$3xy(4x + 5y)$
D.  $3xy(4x + 5y)$
Solution:
$= 12x^2y + 15xy^2$
$= 3xy (4x + 5y)$
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MCQ 1251 Mark
Divide as directed: $5(2x + 1) (3x + 5) ÷ (2x + 1)$
  • ✓
    $5(3x + 5)$
  • B
    $(3x + 5)$
  • C
    $5$
  • D
    None of these.
Answer
Correct option: A.
$5(3x + 5)$
$5(3x + 5)$
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MCQ 1261 Mark
The factors of $49p^2 - 36$ are:
  • A
    $(7p + 6)^2$
  • B
    $(7p - 6)^2$
  • ✓
    $(7p - 6 ) ( 7p + 6)$
  • D
    None of the above.
Answer
Correct option: C.
$(7p - 6 ) ( 7p + 6)$
C.  $(7p - 6 ) ( 7p + 6)$
Solution:
$49p^2 - 36 = (7p)^2 - ( 6 )^2 = (7p - 6 ) ( 7p + 6)$
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MCQ 1271 Mark
The common factor of $x^2y^2$ and $x^3y^3$ is:
  • ✓
    $x^2y^2$
  • B
    $x^3y^3$
  • C
    $x^2y^3$
  • D
    $x^3y^2$
Answer
Correct option: A.
$x^2y^2$
A.  $x^2y^2$
Solution:
$x^2y^2 = x \times x \times y \times y$
$x^3y^3 = x \times x \times x \times y \times y \times y$
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MCQ 1281 Mark
The common factor of $3a^2b^4c^2, 12b^2c^4$ and $15a^3b^4c^4$ is:
  • A
    $b^4c^4$
  • ✓
    $3b^2c^2$
  • C
    $15b^2c^4$
  • D
    $12b^2c^4$
Answer
Correct option: B.
$3b^2c^2$
B.  $3b^2c^2$
Solution:
$3a^2b^4c^2 = 3 \times a \times a \times b \times b \times b \times b \times c \times c$
$12b^2c^4 = 2 \times 2 \times 3 \times b \times b \times c \times c \times c \times c$
$15a^3b^4c^4 = 3 \times 5 \times a \times a \times a \times b \times b \times b \times b \times c \times c \times c \times c$
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MCQ 1291 Mark
If $x = 2,\  y = -1$ then the value of $x^2 + 4xy + 4y^2$ is:
  • ✓
    $0$
  • B
    $1$
  • C
    $-1$
  • D
    $2$
Answer
Correct option: A.
$0$
A.  $0$
Solution:
$=x^2+4 x y+4 y^2=(x)^2+2(x)(2 y)+(2 y)^2 $
$ =(x+2 y)^2=\{2+2(-1)\}^2=0$
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MCQ 1301 Mark
The factors of $a^2 + b - ab - a$ are:
  • A
    $(a + 1)(a - b)$
  • ✓
    $(a - 1)(a - b)$
  • C
    $(a + b)(a - 1)$
  • D
    None.
Answer
Correct option: B.
$(a - 1)(a - b)$
B.  $(a - 1)(a - b)$
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MCQ 1311 Mark
Tick $(\checkmark)$ the correct answer of the following:
$(7a^2 - 63b^2) =\  ?$
  • A
    $(7a - 9b)(9a + 7b)$
  • B
    $(7a - 9b)(7a + 9b)$
  • C
    $9(a - 3b)(a + 3b)$
  • ✓
    $7(a - 3b)(a + 3b)$
Answer
Correct option: D.
$7(a - 3b)(a + 3b)$
D.  $7(a - 3b)(a + 3b)$
Solution:
$7 a^2-63 b^2=7\left(a^2-9 b^2\right) $
$ =7\left\{(a)^2-(3 b)^2\right\}$
$ =7(a-3 b)(a+36)$
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MCQ 1321 Mark
Amrit and Pankaj expanded $(x - 5)^2.$ Amrit's answer is $x^2 - 25$ and Pankaj's answer is $x^2 -10x + 25.$ Which of the following statements is correct?
  • A
    Amrit's answer is correct.
  • B
    Pankaj's answer is wrong.
  • C
    Both got correct answer.
  • ✓
    Pankaj's answer is correct.
Answer
Correct option: D.
Pankaj's answer is correct.
D.  Pankaj's answer is correct.
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MCQ 1331 Mark
Tick $(\checkmark)$ the correct answer:
$(2 - 50x^2) = \ ?$
  • A
    $2(1 - 5x)^2$
  • B
    $2(1 + 5x)^2$
  • C
    $(2 - 5x)(2 + 5x)$
  • ✓
    $2(1 - 5x)(1 + 5x)$
Answer
Correct option: D.
$2(1 - 5x)(1 + 5x)$
D.  $2(1 - 5x)(1 + 5x)$
Solution:
$2-50 x^2=2\left(1-25 x^2\right) $
$ =2\left\{(1)^2-(5 x)^2\right\} $.
$ =2(1-5 x)(1+5 x)$
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MCQ 1341 Mark
One of the factors of $(a2 - b^2) (c^2 - d^2) − 4abcd$ is:
  • ✓
    $(ac - bd + bc + ad)$
  • B
    $ac + bd + bc + ad$
  • C
    $ab + bd - bc - ad$
  • D
    Cannot be determined.
Answer
Correct option: A.
$(ac - bd + bc + ad)$
A.  $(ac - bd + bc + ad)$
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MCQ 1351 Mark
On factorising $14pq + 35pqr,$ we get:
  • A
    $pq(14 + 35r)$
  • B
    $p(14q + 35qr)$
  • C
    $q(14p + 35pr)$
  • ✓
    $7pq(2 + 5r)$
Answer
Correct option: D.
$7pq(2 + 5r)$
$14pq + 35pqr$
$= 2.7.p.q + 5.7.p.q.r$
$= 7pq(2 + 5r)$
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MCQ 1361 Mark
Tick $(\checkmark)$ the correct answer:
$pq^2 + q(p - 1) - 1 = \ ?$
  • A
    $(pq + 1)(q − 1)$
  • B
    $p(q + 1)(q − 1)$
  • C
    $q(p − 1)(q + 1)$
  • ✓
    $(pq − 1) (q + 1)$
Answer
Correct option: D.
$(pq − 1) (q + 1)$
D.  $(pq − 1) (q + 1)$
Solution:
$pq^2 + q(p - 1) - 1$
$= pq^2 + pq - q - 1$
$= pq(q + 1) + -1(q + 1)$
$= (q + 1)(pq - 1)$
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MCQ 1371 Mark
The factorisation of $6x + 12y$ is:
  • ✓
    $6(x + 2y)$
  • B
    $3(x + 4y)$
  • C
    $2(3x + 12y)$
  • D
    None of these.
Answer
Correct option: A.
$6(x + 2y)$

$6x + 12y = 6(x + 2y)$

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MCQ 1381 Mark
Divide $x(4x^2 - 100)$ by $4x(x + 5)$
  • ✓
    $(x - 5)$
  • B
    $(x^2 - 25)$
  • C
    $(x + 5)$
  • D
    $(x + 5)^2$
Answer
Correct option: A.
$(x - 5)$
A.  $(x - 5)$
Solution:
$\frac{\text{x}(4\text{x}^2-100)}{\text{x}(\text{x}-5)}$
$\Rightarrow\frac{\text{x}((2\text{x})^2-(10)^2)}{4\text{x}(\text{x}+5)}$
$\Rightarrow\frac{\text{x}(2\text{x}+10)(\text{2x}-10)}{4\text{x}(\text{x}+5)}$
$\Rightarrow\frac{2\text{x}(\text{x}+5)(2\text{xx}-10)}{2\times2\text{x}(\text{x}+5)}$
Cancel the common factors
$\Rightarrow\frac{2(\text{x}-5)}{2}=(\text{x}-5)$
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MCQ 1391 Mark
What is $12ab^2 \div c^3 8bc^2$
  • ✓
    $3abc$
  • B
    $3bc$
  • C
    $\frac{1}{3}\text{bc}$
  • D
    $\frac{1}{3}\text{abc}$
Answer
Correct option: A.
$3abc$
A.  $3abc$
Solution:
The given expression can be written in fractional fonn as shown below,
$\frac{24\text{ab}^2\text{c}^2}{8\text{bc}^2},$ Now find the Highest Common Factor of the numerator and denominator,
$\Rightarrow \frac{8\times3\times\text{a}\times\text{b}^2\times\text{c}^2}{8\times\text{b}\times\text{c}^2}=3\text{abc}$
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MCQ 1401 Mark
When we factorise $^x2 + 5x + 6,$ then we get:
  • ✓
    $(x + 2) (x + 3)$
  • B
    $(x - 2) (x - 3)$
  • C
    $(x × 2) + (x × 3)$
  • D
    $(x × 2) - (x × 3)$
Answer
Correct option: A.
$(x + 2) (x + 3)$
A.  $(x + 2) (x + 3)$
Solution:
The factors of a form:
$(x + a) (x + b) = x^2 + (a + b) x + ab$
$x^2+ 5x + 6$
$a + b = 5$ and $ab = 6$
$x^2 + 5x + 6 = (x + 2) (x + 3)$
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MCQ 1411 Mark
Find the value of x from $\frac{8\text{x}+4}{4}=8\text{x}$
  • A
    $-\frac{1}{6}$
  • B
    $\frac{1}{10}$
  • C
    $0$
  • ✓
    $\frac{1}{6}$
Answer
Correct option: D.
$\frac{1}{6}$

$\frac{8\text{x}+4}{4}=8\text{x}$
Multiply $4$ on both sides
$\Rightarrow 8x + 4 = 32x$
Bring like terms together
$\Rightarrow 4 = 32x - 8x$
$\Rightarrow 4 = 24x$
$\Rightarrow\text{x}=\frac{4}{24}=\frac{1}{6}$

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MCQ 1421 Mark
The common factor of $24a^3b^4, 36a^4c^4$ and $48a^3b^2c$ is:
  • A
    $24a^3$
  • B
    $36a^3$
  • ✓
    $12a^3$
  • D
    $48a^3$
Answer
Correct option: C.
$12a^3$
C.  $12a^3$
Solution:
$24a^3b^4 = 2 \times 2 \times 2 \times 3 \times a \times a \times a \times b \times b \times b \times b$
$36a^4c^4 = 2 \times 2 \times 3 \times 3 \times a \times a \times a \times a \times c \times c \times c \times c$
$48a^3b^2c = 2 \times 2 \times 2 \times 2 \times 3 \times a \times a \times a \times b \times b \times c$
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MCQ 1431 Mark
Choose the factors of $15x^2 - 26x + 8$ from the following.
  • A
    $(3x - 4), (5x + 2)$
  • ✓
    $(3x - 4), (5x - 2)$
  • C
    $(3x + 4), (5x - 2)$
  • D
    $(3x + 4), (5x + 2)$
Answer
Correct option: B.
$(3x - 4), (5x - 2)$
B.  $(3x - 4), (5x - 2)$
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MCQ 1441 Mark
The common factor of $a^2m^4$ and $a^4m^2$ is:
  • A
    $a^4m^4$
  • ✓
    $a^2m^2$
  • C
    $a^2m^4$
  • D
    $a^4m^2$
Answer
Correct option: B.
$a^2m^2$
B.  $a^2m^2$
Solution:
$a^2m^4 = a \times a \times m \times m \times m \times m$
$a^4m^2 = a \times a \times a \times a \times m \times m$
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MCQ 1451 Mark
The factorisation of $(lm + l) + m + 1$ is:
  • ✓
    $(l + 1) (m + 1)$
  • B
    $(l - 1) (m - 1)$
  • C
    $(l + 1) (m - 1)$
  • D
    $(l - 1) (m + 1)$
Answer
Correct option: A.
$(l + 1) (m + 1)$

$= l(m + 1) + 1 (m + 1)$
$= (l + 1 ) (m + 1)$

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MCQ 1461 Mark
Find and correct the errors in the following mathematical statements.$ x + 2x + 3x = 5x$
  • A
    $x + 2x + 3x = 7x$
  • ✓
    $x + 2x + 3x = 6x$
  • C
    $x + 2x + 3x = 1/2x$
  • D
    $x + 2x + 3x = 5x$
Answer
Correct option: B.
$x + 2x + 3x = 6x$
$x + 2x + 3x = 6x$
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MCQ 1471 Mark
One of the factors of $x^4 + 4$ is:
  • ✓
    $x^2 - 2x +2$
  • B
    $x^2 + 2$
  • C
    $x^2 - 2$
  • D
    None of these.
Answer
Correct option: A.
$x^2 - 2x +2$
A.  $x^2 - 2x +2$
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MCQ 1481 Mark
The value of $3.5 \times 3.5 - 2.5 \times 2.5$ is:
  • A
    $-6$
  • ✓
    $6$
  • C
    $60$
  • D
    $1$
Answer
Correct option: B.
$6$

Value$ = (3.5 + 2.5) (3.5 - 2.5) = 6$

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MCQ 1491 Mark
The factorisation of $a(x + y + z) + b(x + y + z) + c(x + y + z)$ is:
  • ✓
    $(a + b + c) (x + y + z)$
  • B
    $(ab + bc + ca) (x + y + z)$
  • C
    $(xy + yz + zx) (a + b + c)$
  • D
    None of these.
Answer
Correct option: A.
$(a + b + c) (x + y + z)$

$a(x + y + z) + b(x + y + z) + c(x + y + z)$
$= (x + y + z) (a + b + c)$

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MCQ 1501 Mark
The common factor of $36p^2q^3x^4, 48pq^3x^2$ and $54p^3q^3x^4$ is:
  • ✓
    $6pq^3x^2$
  • B
    $36pq^3x^2$
  • C
    $54pq^3x^2$
  • D
    $48pq^3x^2$
Answer
Correct option: A.
$6pq^3x^2$
A.  $6pq^3x^2$
Solution:
$36 p^2 q^3 x^4=2 \times 2 \times 3 \times 3 \times p \times p \times q \times q \times q \times x \times x \times x \times x $
$ 48 p q^3 x^2=2 \times 2 \times 2 \times 2 \times 3 \times p \times q \times q \times q \times x \times x $
$ p^3 q^3 x^4=p \times p \times p \times q \times q \times q \times x \times x \times x \times x$
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MCQ 1511 Mark
Divide $36(a^2bc + ab^2c + abc^2)$ by $9abc$
  • A
    $4abc + 4abc + 4abc$
  • B
    $36a + 36b + 36c$
  • ✓
    $4(a + b + c)$
  • D
    $4abc + 4ab^2c + 4abc^2$
Answer
Correct option: C.
$4(a + b + c)$
C.  $4(a + b + c)$
Solution:
Write this division as a fraction$\frac{36(\text{a}^2\text{bc}+\text{ab}^2\text{c}+\text{abc}^2)}{9\text{abc}}$
Take out the common factors from the numerator.
$\Rightarrow\frac{9\times4\text{abc}(\text{a+b+c})}{9\text{abc}}$
$\Rightarrow4(\text{a+b+c})$
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MCQ 1521 Mark
The factorisation of $5x - 20$ is:
  • A
    $5(x - 5)$
  • B
    $5(x - 3)$
  • ✓
    $5(x - 4)$
  • D
    $5(x - 20)$
Answer
Correct option: C.
$5(x - 4)$

$5x - 20 = 5 (x - 4)$

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MCQ 1531 Mark
Tick $(\checkmark)$ the correct answer:
$a^2 + bc + ab + ac = ?$
  • ✓
    $(a + b)(a + c)$
  • B
    $(a + b)(b + c)$
  • C
    $(b + c)(c + a)$
  • D
    $a(a + b + c)$
Answer
Correct option: A.
$(a + b)(a + c)$
A.  $(a + b)(a + c)$
Solution:
$a^2 + bc + ab + ac$
$= a^2 + ab + ac + bc$
$= a(a + b) + c(a + b)$
$= (a + b)(a + c)$$
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MCQ 1541 Mark
The factorisation of $x^2 + xy + 2x + 2y$ is:
  • ✓
    $(x + 2)(x + y)$
  • B
    $(x + 2)(x y)$
  • C
    $(x - 2)(x + y)$
  • D
    $(x - 2)(x - y)$
Answer
Correct option: A.
$(x + 2)(x + y)$
A.  $(x + 2)(x + y)$
Solution:
$= x^2 + xy + 2x + 2y$
$= x(x + y) + 2(x + y)$
$= (x + 2) (x + y)$
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MCQ 1551 Mark
The factorisation of $1 + p + q + r + pq + qr + pr + pqr$ is:
  • ✓
    $(1 + p) (1 + q) (1 + r)$
  • B
    $(1 - p) (1 - q) (1 - r)$
  • C
    $(1 - p) (1 - q) (1 + r)$
  • D
    $(1 + p) (1 - q) (1 - r)$
Answer
Correct option: A.
$(1 + p) (1 + q) (1 + r)$
$= 1 + p + q + r + pq + qr+pr + pqr$
$= 1 + p + q + pq + r(1 + p + q + pq)$
$= (1 + r) (1 + p + q + pq)$
$= (1 + r) (1 + p) (1 + q)$
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MCQ 1561 Mark
$105p^2q^2r^2\ (p + q)\  (q + r)\  (r + p) \div 21pq\  (q + r)\  (r + p)$
  • A
    $5pq(p \div q)$
  • ✓
    $5pqr^2(p + q)$
  • C
    $\frac{1}{5\text{pq}(\text{p}+\text{q})}$
  • D
    $\frac{1}{5\text{pqr}(\text{p}+\text{q})}$
Answer
Correct option: B.
$5pqr^2(p + q)$
B.  $5pqr^2(p + q)$
Solution:
Express the division as a fraction
$\frac{105\text{p}^2\text{q}^2\text{r}^2(\text{p}+\text{q})(\text{q}+\text{r})(\text{r}+\text{p})}{21\text{pq}(\text{q}+\text{r})(\text{r}+\text{p})}$
$\Rightarrow\frac{21\times5\text{p}^2\text{q}^2\text{r}^2(\text{p}+\text{q})(\text{q}+\text{r})(\text{r}+\text{p})}{21\text{pq}(\text{q}+\text{r})(\text{r}+\text{p})}$
Cancel the common factors from the numerator and denominator
$\Rightarrow\frac{21\times5\text{p}^2\text{q}^2\text{r}^2(\text{p}+\text{q})}{21\text{pq}}$
Cancel the common factors from the numerator and denominator
$\Rightarrow5\text{pqr}^2(\text{p}+\text{q})$
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MCQ 1571 Mark
Find and correct the errors in the following mathematical statements. $2x + 3y = 5xy$
  • A
    $2x + 3y = 6xy$
  • B
    $2x + 3y = 2x - 3y$
  • ✓
    $2x + 3y = 2x + 3y$
  • D
    None of these
Answer
Correct option: C.
$2x + 3y = 2x + 3y$
$2x + 3y = 2x + 3y$
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MCQ 1581 Mark
One of the factors of $x^7 + xy^6$ is:
  • A
    $y$
  • B
    $x$
  • ✓
    $x^2 + y^2$
  • D
    None of these.
Answer
Correct option: C.
$x^2 + y^2$
C.  $x^2 + y^2$
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MCQ 1591 Mark
The factorisation of $(l + m)^2 - 4lm$ is:
  • ✓
    $(l – m)^2$
  • B
    $(l + m - 2)^2$
  • C
    $(l + m + 2)^2$
  • D
    None of these.
Answer
Correct option: A.
$(l – m)^2$
A.  $(l - m)^2$
Solution:
$= (1 + m)^2 - 4lm$
$= l^2 + m^2 + 2lm - 4lm$
$= l^2 - 2lm + m^2 = (l - m)^2$
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MCQ 1601 Mark
The factorisation of $28a^3b^5 - 42a^5b^3$ is:
  • ✓
    $14a^3b^3(2b^2 - 3a^2)$
  • B
    $14a^2b^3(2b^2 - 3a^2)$
  • C
    $14a^3b^2(2b^2 - 3a^2)$
  • D
    None of these.
Answer
Correct option: A.
$14a^3b^3(2b^2 - 3a^2)$
A.  $14a^3b^3(2b^2 - 3a^2)$
Solution:
$28a^3 b^5 - 42a^5b^3$
​​​​​​​$ = 14a^2b^3(2b^2 - 3a^2)$
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MCQ 1611 Mark
The common factor of $a^3b^2$ and $a^4b$ is:
  • ✓
    $a^3b$
  • B
    $a^4b^2$
  • C
    $a^4b$
  • D
    $a^3b^2$
Answer
Correct option: A.
$a^3b$
A.  $a^3b$
Solution:
Same as question no. $11$
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MCQ 1621 Mark
The factorisation of $3x^2 + 10x + 8$ is:
  • ✓
    $(3x + 4) (x + 2)$
  • B
    $(3x - 4) (x – 2)$
  • C
    $(3x + 4) (x - 2)$
  • D
    $(3x - 4) (x + 2)$
Answer
Correct option: A.
$(3x + 4) (x + 2)$
A.  $(3x + 4) (x + 2)$
Solution:
$= 3x^2 + 10x + 8 = 3x^2 + 6x + 4x + 8$
$= 3x(x + 2) + 4(x + 2)$
$= (x + 2) (3x + 4).$
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MCQ 1631 Mark
The factorisation $1 + 16x + 64x^2$ is:
  • A
    $(1 - 8x)^2$
  • ✓
    $(1 + 8x)^2$
  • C
    $(8 - x)^2$
  • D
    $(8 + x)^2$
Answer
Correct option: B.
$(1 + 8x)^2$
B.  $(1 + 8x)^2$
Solution:
$1 + 16x + 64x^2$
$= (1)2 + 2(1) (8x) + (8x)^2 = (1 + 8x)^2$
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MCQ 1641 Mark
The factorisation of $x^2y^2 + xy + xy^2z + yz + x^2yz + xz$ is:
  • ✓
    $(xy + yz + zx) (xy + 1)$
  • B
    $(xy + yz + zx) (yz + 1)$
  • C
    $(xy + yz + zx) (zx + 1)$
  • D
    None of these.
Answer
Correct option: A.
$(xy + yz + zx) (xy + 1)$
A.  $(xy + yz + zx) (xy + 1)$
Solution:
$= x^2y^2 + xy + xy^2z + yz + x^2yz + xz$
$= xy(xy + 1) + yz(xy + 1) + zx(xy + 1)$
$= (xy + yz + zx) (xy + 1)$
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MCQ 1651 Mark
Which of the following is a factor of $m^4 - 256?$
  • A
    $m + 4$
  • B
    $m^2 + 4$
  • C
    $m^2 - 4$
  • ✓
    $m + 16$
Answer
Correct option: D.
$m + 16$
D.  $m + 16$
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MCQ 1661 Mark
The factors of $3m^2 + 9m + 6$ are:
  • A
    $(m + 1) (m + 2)$
  • B
    $6(m + 1) (m + 2)$
  • ✓
    $3(m + 1) (m + 2)$
  • D
    $9(m + 1) (m + 2)$
Answer
Correct option: C.
$3(m + 1) (m + 2)$
C.  $3(m + 1) (m + 2)$
Solution:
$3m^2 + 9m + 6 = 3(m^2 + 3m + 2)$
$= 3 [m^2 + m + 2m + 2]$
$= 3 [m(m + 1) + 2( m + 1)]$
$= 3 [(m + 1) (m + 2)]$
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MCQ 1671 Mark
The factorisation of $3x^2 - 16x + 16$ is:
  • ✓
    $(x - 4) (3x - 4)$
  • B
    $(x + 4) (3x + 4)$
  • C
    $(x - 4) (3x + 4)$
  • D
    $(x + 4) (3x - 4)$
Answer
Correct option: A.
$(x - 4) (3x - 4)$
A.  $(x - 4) (3x - 4)$
Solution:
$= 3x^2 - 16x + 16$
$= 3x^2 - 12x - 4x + 16$
$= 3x(x - 4) - 4(x - 4)$
$= (x - 4) (3x - 4)$
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MCQ 1681 Mark
Which of the following arc the factors of $1 - x^2?$
  • A
    $(x + 1) (x - 1)$
  • ✓
    $(1 - x) (1 + x)$
  • C
    $(1 - x) (1 - x)$
  • D
    $(1 + x) (1 + x)$
Answer
Correct option: B.
$(1 - x) (1 + x)$
B.  $(1 - x) (1 + x)$
View full question & answer→
MCQ 1691 Mark
The common factors of $10a, 20b$ and $30c$ are:
  • ✓
    $10$
  • B
    $ab$
  • C
    $ac$
  • D
    $10$abc
Answer
Correct option: A.
$10$
$10a = 2 \times 5 \times a$
$20b = 2 \times 2 \times 5 \times b$
$30c = 2 \times 3 \times 5 \times c$
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MCQ 1701 Mark
Which of the following is quotient obtained on dividing $-18 xyz^2$ by $-3xz?$
  • ✓
    $6yz$
  • B
    $-6yz$
  • C
    $6xy^2$
  • D
    $6xy$
Answer
Correct option: A.
$6yz$
A.  $6yz$
Solution:
$\frac{-18\text{xyz}^2}{-3\text{xz}}$
$\frac{-3\times6\times\text{z}\times\text{x}\times\text{z}}{-3\times\text{x}\times\text{z}}$
$=\frac{6\times\text{y}\times\text{z}}{1}$
$=6\text{yz}$
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MCQ 1711 Mark
The factorisation of $a^3 + a^2b + ab^2$ is:
  • ✓
    $a(a^2 + ab + b^2)$
  • B
    $6(a^2 + ab + b^2)$
  • C
    $ab(a^2 + ab + b^2)$
  • D
    None of these.
Answer
Correct option: A.
$a(a^2 + ab + b^2)$
A.  $a(a^2 + ab + b^2)$
Solution:
$a^2 + a^2b + ab^2 $
$= a(a^2 + ab + b^2)$
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MCQ 1721 Mark
The common factor of $14a^2b$ and $35a^4b^2$ is:
  • A
    $a^4b^2$
  • B
    $35a^4b^2$
  • C
    $14a^2b$
  • ✓
    $7a^2b$
Answer
Correct option: D.
$7a^2b$
D.  $7a^2b$
Solution:
$14 a^2 b=2 \times 7 \times a \times a \times b $
$ 35 a^4 b^2=5 \times 7 \times a \times a \times a \times a \times b \times b$
View full question & answer→
MCQ 1731 Mark
Which of the following is the common factor of $5xy, 3pqr$ and $40xyz?$
  • A
    $5$
  • B
    $0$
  • C
    $xy$
  • ✓
    $1$
Answer
Correct option: D.
$1$
$5xy = 5 \times 1 \times x \times y$
$3pqr = 3 \times 1 \times p \times q \times r$
$40xyz = 20 \times 2 \times 1 \times x \times y \times z$
Thus, the common factors are common factors of $1.$
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MCQ 1751 Mark
Tick $(\checkmark)$ the correct answer:
$1 - 2ab - (a^2 + b^2) = ?$
  • A
    $(1 + a - b)(1 + a + b)$
  • B
    $(1 + a + b)(1 - a + b)$
  • ✓
    $(1 + a + b)(1 - a - b)$
  • D
    $(1 + a - b)(1 - a + b)$
Answer
Correct option: C.
$(1 + a + b)(1 - a - b)$
C.  $(1 + a + b)(1 - a - b)$
Solution:
$1 - 2ab - (a^2 + b^2)$
$= 1 - 2ab - a^2- b^2$
$= 1 - (a^2+ b^2 + 2ab)$
$= 1 - (a + b)^2$
$= (1 + a + b)(1 - a - b)$
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MCQ 1761 Mark
If $3x + 3y = 24$ and $2x - 3y = 12$ then the value of $xy$ is:
  • A
    $10$
  • ✓
    $18$
  • C
    $14$
  • D
    $12$
Answer
Correct option: B.
$18$
$18$
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MCQ 1771 Mark
On factorising $14pq + 35pqr$, we get:
  • A
    $pq(14 + 35r)$
  • ✓
    $7pq(2 + 5r)$
  • C
    $p(14q + 35qr)$
  • D
    $q(14p + 35pr)$
Answer
Correct option: B.
$7pq(2 + 5r)$

$= 14pq + 35pqr$
$= 2.7.p.q + 5.7.p.q.r$
$= 7pq(2 + 5r)$

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MCQ 1781 Mark
Which of the following is a factor of $6xy - 4y + 6 - 9x?$
  • A
    $2x + y$
  • B
    $x - y$
  • C
    $2x - 3$
  • ✓
    $3x - 2$
Answer
Correct option: D.
$3x - 2$
$3x - 2$
View full question & answer→
MCQ 1791 Mark
Factorise: $10x^2 - 18x^3 + 14x4$
  • A
    $2x^2$
  • B
    $2x^2(9x^2 - 5x + 7)$
  • C
    $(7x^2 - 9x + 5)$
  • ✓
    $2x^2(7x^2 - 9x + 5)$
Answer
Correct option: D.
$2x^2(7x^2 - 9x + 5)$
D.  $2x^2(7x^2 - 9x + 5)$
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MCQ 1801 Mark
$x^9 - x$ is having:
  • A
    $4$ factors.
  • B
    $2$ factors.
  • ✓
    $5$ factors.
  • D
    Cannot be determined.
Answer
Correct option: C.
$5$ factors.
C.  $5$ factors.
View full question & answer→
MCQ 1811 Mark
Obtain the factors of $x^2 + 6x + 8$
  • ✓
    $(x + 2) (x + 4)$
  • B
    $(x^2 + 4) (x + 4)$
  • C
    $(3x + 4) (x + 2)$
  • D
    $(x - 2) (x - 4)$
Answer
Correct option: A.
$(x + 2) (x + 4)$
A.  $(x + 2) (x + 4)$
Solution:
Split the middle terms of the given expression such that the product of the terms after splitting the middle terms is the same as the product of the first term and the last term and the sum of the terms after splitting the middle term is the same as the middle term.
$= x^2 + 4x + 2x + 8$
$= x(x + 4) + 2(x + 4)$
$= x(x + 2) (x + 4)$
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MCQ 1821 Mark
Which of the following is a factor of $y^2 - 7y + 12?$
  • A
    $2y + 3$
  • B
    $y + 3$
  • ✓
    $y - 3$
  • D
    $2y - 2$
Answer
Correct option: C.
$y - 3$
C.  $y - 3$
View full question & answer→
MCQ 1831 Mark
$(y – x) (y + x)$ is equal to which of the following:
  • A
    $y^2 - yx$
  • B
    $yx - x^2$
  • ✓
    $y^2 - x^2$
  • D
    $x^2 - y^2$
Answer
Correct option: C.
$y^2 - x^2$
C.  $y^2 - x^2$
Solution:
$= (y - x) (y + x)$
$= y^2 - Xy + Xy - x^2$
$= y^2 - x^2$
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MCQ 1841 Mark
Sam is stuck at an equation $4a + a - 2a = 72$, help him find the value of a.
  • A
    $10.2$
  • B
    $72$
  • ✓
    $24$
  • D
    $14.4$
Answer
Correct option: C.
$24$

Given equation is,
$4a + a - 2a = 72$
Solve the like terms.
$\Rightarrow 5a - 2a = 72$
$\Rightarrow 3a = 72$
$\Rightarrow a = 24$

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MCQ 1851 Mark
The factorisation of $ab - a - b + 1$ is:
  • ✓
    $(a - 1) (b - 1)$
  • B
    $(a + 1) (b + 1)$
  • C
    $(a - 1) (b + 1)$
  • D
    $(a + 1) (b - 1)$
Answer
Correct option: A.
$(a - 1) (b - 1)$

$= ab - a - b + 1$
$= a(b - 1) - 1(b - 1)$
$= (a - 1) (b - 1)$

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MCQ 1861 Mark
Factorize $55xz^2 + 99x^3z$
  • A
    $11(5xz^2 + 9x^3z)$
  • B
    $11x^3z^2(5x) + 9z)$
  • ✓
    $11xz(5z + 9x^2)$
  • D
    $5(11xz^2) + 9(11x^3z)$
Answer
Correct option: C.
$11xz(5z + 9x^2)$
C.  $11xz(5z + 9x^2)$
Solution:
In the given expression, $11xz$ is the common factor.
Hence after factorization we can rewrite the expression as $11xz(5z + 9x^2).$
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MCQ 1871 Mark
What is the value of $2x - 3y + 4z$ at $x = 2, y = 0 \& z = 1$
  • A
    $4$
  • B
    $6$
  • ✓
    $8$
  • D
    $10$
Answer
Correct option: C.
$8$
$8$
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MCQ 1881 Mark
Tick $(\checkmark)$ the correct answer:
$y^2 + 2y - 3 = ?$
  • A
    $(y - 1)(y + 3)$
  • ✓
    $(y + 1)(y - 3)$
  • C
    $(y - 1)(y - 3)$
  • D
    $(y + 2)(y - 3)$
Answer
Correct option: B.
$(y + 1)(y - 3)$
B.  $(y - 1)(y + 3)$
Solution:
$y^2 + 2y - 3$
${-3 = 3 \times (-1), 2 = 3 - 1}$
$= y^2+ 3y - y - 3$
$= y(y + 3) - 1(y + 3)$
$= (y - 1)(y + 3)$
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MCQ 1891 Mark
The factors of $3 \mathrm{m}^{2}+9 \mathrm{m}+6$ are:
  • A
    $(m+1)(m+2)$
  • ✓
    $3(m+1)(m+2)$
  • C
    $6(m+1)(m+2)$
  • D
    $9(m+1)(m+2)$
Answer
Correct option: B.
$3(m+1)(m+2)$
b$3 m^{2}+9 m+6=3\left(m^{2}+3 m+2\right)$ $=3\left[m^{2}+m+2 m+2\right]$ $=3[m(m+1)+2(m+1)]$ $=3[(m+1)(m+2)]$
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MCQ 1901 Mark
When we factorise $x^{2}+5 x+6$, then we get:
  • ✓
    $(x+2)(x+3)$
  • B
    $(x-2)(x-3)$
  • C
    $(x \times 2)+(x \times 3)$
  • D
    $(x \times 2)-(x \times 3)$
Answer
Correct option: A.
$(x+2)(x+3)$
aThe factors of a form: $\left(x+(a)\left(x+(b)=x^{2}+(a+(b) x+a b)\right.\right.$ $x^{2}+5 x+6$ $a+b=5$ and $a b=6$ $x^{2}+5 x+6=(x+2)(x+3)$
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MCQ 1911 Mark
The factors of $\mathrm{m}^{2}-256$ are:
  • A
    $(m+4)^{2}$
  • B
    $(m-4)^{2}$
  • C
    $(m-4)(m+4)$
  • ✓
    None of the above
Answer
Correct option: D.
None of the above
d
$\mathrm{m}^{4}=\left(\mathrm{m}^{2}\right)^{2}$ and $256=(16)^{2}$
$\mathrm{m}^{4}-256=\left(\mathrm{m}^{2}\right)^{2}-(16)^{2}=\left(\mathrm{m}^{2}-16\right)\left(\mathrm{m}^{2}+16\right)$
$\mathrm{m}^{2}-16=\mathrm{m}^{2}-4^{2}=(\mathrm{m}-4)(\mathrm{m}+4)$
$\mathrm{m}^{4}-256=(\mathrm{m}-4)(\mathrm{m}+4)\left(\mathrm{m}^{2}+16\right)$
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MCQ 1921 Mark
The factors of $49 \mathrm{p}^{2}-36$ are:
  • A
    $(7 p+6)^{2}$
  • B
    $(7 p-6)^{2}$
  • ✓
    $(7 p-6)(7 p+6)$
  • D
    None of the above
Answer
Correct option: C.
$(7 p-6)(7 p+6)$
c
$49 p^{2}-36=(7 p)^{2}-(6)^{2}=(7 p-6)(7 p+6)$
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MCQ 1931 Mark
The factors of $4 y^{2}-12 y+9$ is:
  • A
    $(2 y+3)^{2}$
  • ✓
    $(2 y-3)^{2}$
  • C
    $(2 y-3)(2 y+3)$
  • D
    None of the above
Answer
Correct option: B.
$(2 y-3)^{2}$
b
$4 y^{2}-12 y+9$
$4 y^{2}=(2 y)^{2} \& 9=3^{2} \& 12 y=2.3 \cdot 2 y$
$4 y^{2}-12 y+9=(2 y)^{2}-2 \times 3 \times(2 y)+(3)^{2}$
$=(2 y-3)^{2}$ [By algebraic identities: $\left(\mathrm{a}-(\mathrm{b})^{2}=\mathrm{a}^{2}+\mathrm{b}^{2}-2 \mathrm{ab}\right.$
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MCQ 1941 Mark
The factors of $x^{2}+x y+8 x+8 y$ are:
  • ✓
    $(x+y)(x+8)$
  • B
    $(2 x+y)(x+8)$
  • C
    $(x+2 y)(x+8)$
  • D
    $(x+y)(2 x+8)$
Answer
Correct option: A.
$(x+y)(x+8)$
a
$x^{2}+x y+8 x+8 y$
$=x(x+y)+8(x+y)$
$=(x+y)(x+8)$
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MCQ 1951 Mark
The factors of $6 x y-4 y+6-9 x$ are:
  • A
    $(3 x+2)(2 y+3)$
  • ✓
    $(3 x-2)(2 y-3)$
  • C
    $(3 x-2)(2 y+3)$
  • D
    $(3 x+2)(2 y-3)$
Answer
Correct option: B.
$(3 x-2)(2 y-3)$
b
$6 x y-4 y+6-9 x$
$=6 x y-4 y-9 x+6$
$=2 y(3 x-2)-3(3 x-2)$
$=(3 x-2)(2 y-3)$
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MCQ 1961 Mark
On factorising $14 \mathrm{pq}+35$ pqr, we get:
  • A
    $\mathrm{pq}(14+35 r)$
  • B
    $\mathrm{p}(14 \mathrm{q}+35 \mathrm{qr})$
  • C
    $\mathrm{q}(14 \mathrm{p}+35 \mathrm{pr})$
  • ✓
    $7 \mathrm{pq}(2+5 \mathrm{r})$
Answer
Correct option: D.
$7 \mathrm{pq}(2+5 \mathrm{r})$
$14pq + 35pqr$
$=2.7 . p . q+5.7 . p . q . r$
$=7 \mathrm{pq}(2+5 r)$
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MCQ 1971 Mark
The factorisation of $12 x+36$ is
  • ✓
    $12(x+3)$
  • B
    $12(3 x)$
  • C
    $12(3 x+1)$
  • D
    $x(12+36 x)$
Answer
Correct option: A.
$12(x+3)$
a
$12 x+36$
$12 x+12.3$
$=12(x+3)$
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MCQ 1981 Mark
The factorisation of $12 a^{2} b+15 a b^{2}$ gives:
  • A
    $3 a b(4 a b+5)$
  • B
    $3 a b(4 a+5$
  • C
    $3 a(4 a+5(b)$
  • ✓
    $3 b(4 a+5(b)$
Answer
Correct option: D.
$3 b(4 a+5(b)$
d
$12 a^{2} b+15 a b^{2}$
$12 a^{2} b=3 \times 4 \times a \times a \times b$
$15 a b^{2}=3 \times 5 \times a \times b \times b$
The common factors are $3 a b$.
$12 a^{2} b+15 a b^{2}=3 a b(4 a+5 b)$
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MCQ 1991 Mark
The quotient of $12 a^{8} b^{8}+\left(-a^{6} b^{6}\right)$ is
  • A
    $3 a^{2} b^{2}$
  • B
    $3 a^{2} b$
  • C
    $3 a b^{2}$
  • ✓
    $-3 a^{2} b^{2}$
Answer
Correct option: D.
$-3 a^{2} b^{2}$
d
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MCQ 2001 Mark
The quotient of $28 x^{2}+14 x$ is
  • A
    $2$
  • ✓
    $2 x$
  • C
    $x$
  • D
    $x^{2}$
Answer
Correct option: B.
$2 x$
$\frac{28 x^{2} 1}{14 x}=\frac{2 \times 2 \times 7 \times x \times x}{2 \times 7 \times x}=2 \times$
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MCQ 2011 Mark
If $x=2, y=-1$ then the value of $x^{2}-4 x y+4 y^{2}$ is
  • ✓
    $0$
  • B
    $1$
  • C
    $-1$
  • D
    $2$
Answer
Correct option: A.
$0$
$x^{2}+4 x y+4 y^{2}=(x)^{2}+2(x)(2 y)+(2 y)^{2}$
$=(x+2 y)^{2}=\{2+2(-1)\}^{2}=0$
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MCQ 2021 Mark
If $\left(x-\frac{1}{x}\right)^{2}=x^{2}+a+\frac{1}{x^{2}}$ then $a=$
  • ✓
    -2
  • B
    2
  • C
    $2 x$
  • D
    $-2 x$
Answer
Correct option: A.
-2
$\left(x-\frac{1}{x}\right)^{2}=x^{2}-2+\frac{1}{x^{2}} \therefore a=-2$
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MCQ 2031 Mark
The value of $3.5 \times 3.5-2.5 \times 2.5$ is
  • A
    $-6$
  • ✓
    $6$
  • C
    $60$
  • D
    $1$
Answer
Correct option: B.
$6$
Value $=(3.5+2.5)(3.5-2.5)=6 $
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MCQ 2041 Mark
If $x^{2}-x-42=(x+k)(x+6),$ then $k=$
  • A
    $6$
  • B
    $-6$
  • C
    $7$
  • ✓
    $-7$
Answer
Correct option: D.
$-7$
$x^{2}-x-42$
$=x^{2}-7 x+6 x-42$
$=x(x-7)+6(x-7)$
$=(x-7)(x+6) \therefore k=-7$
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MCQ 2051 Mark
The factorisation of $6-x-2 x^{2}$ is
  • ✓
    $(2+x)(3-2 x)$
  • B
    $(2+x)(3+2 x)$
  • C
    $(2-x)(3-2 x)$
  • D
    $(2-x)(3+2 x)$
Answer
Correct option: A.
$(2+x)(3-2 x)$
a
$6-x-2 x^{2}$
$=6+3 x-4 x-2 x^{2}$
$=3(2+x)-2 x(2+x)$
$=(2+x)(3-2 x)$
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MCQ 2061 Mark
The factorisation of $6 x^{2}-5 x-6$ is
  • ✓
    $(2 x-3)(3 x+2)$
  • B
    $(2 x+3)(3 x+2)$
  • C
    $(2 x-3)(3 x-2)$
  • D
    $(2 x+3)(3 x-2)$
Answer
Correct option: A.
$(2 x-3)(3 x+2)$
a
$6 x^{2}-5 x-6$
$=6 x^{2}-9 x+4 x-6$
$=3 x(2 x-3)+2(2 x-3)$
$=(2 x-3)(3 x+2)$
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MCQ 2071 Mark
The factorisation of $3 x^{2}-16 x+16$ is
  • ✓
    $(x-4)(3 x-4)$
  • B
    $(x+4)(3 x+4)$
  • C
    $(x-4)(3 x+4)$
  • D
    $(x+4)(3 x-4)$
Answer
Correct option: A.
$(x-4)(3 x-4)$
a
$3 x^{2}-16 x+16$
$=3 x^{2}-12 x-4 x+16$
$=3 x(x-4)-4(x-4)$
$=(x-4)(3 x-4)$
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MCQ 2081 Mark
The factorisation of $3 x^{2}+10 x+8$ is
  • ✓
    $(3 x+4)(x+2)$
  • B
    $(3 x-4)(x-2)$
  • C
    $(3 x+4)(x-2)$
  • D
    $(3 x-4)(x+2)$
Answer
Correct option: A.
$(3 x+4)(x+2)$
a
$3 x^{2}+10 x+8=3 x^{2}+6 x+4 x+8$
$=3 x(x+2)+4(x+2)$
$=(x+2)(3 x+4)$
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MCQ 2091 Mark
The value of $(0.68)^{2}-(0.32)^{2}$ is
  • A
    $-1$
  • B
    $0$
  • C
    $1$
  • ✓
    $36$
Answer
Correct option: D.
$36$
$(0.68+0.32)(0.68-0.32)=0.36$
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MCQ 2101 Mark
The value of $\frac{0.564 \times 0.564 \times-0.436 \times 0.436}{0.564-0.436}$ is
  • A
    $0$
  • ✓
    $1$
  • C
    $-1$
  • D
    none of these
Answer
Correct option: B.
$1$
Value $=\frac{(0.564+0.436)(0.564-0.436)}{0.564-0.436}=1$
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MCQ 2111 Mark
The factorisation of $36 x^{2} y^{2}-1$ is
  • ✓
    $(6 x y-1)(6 x y+1)$
  • B
    $(6 x y-1)^{2}$
  • C
    $(6 x y+1)^{2}$
  • D
    $(6+x y)^{2}$
Answer
Correct option: A.
$(6 x y-1)(6 x y+1)$
a
$36 x^{2} y^{2}-1=(6 x y)^{2}-(1)^{2}$
$=(6 x y-1)(6 x y+1)$
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MCQ 2121 Mark
The factorisation of $x^{2}-9$ is
  • A
    $(x-3)^{2}$
  • B
    $(x+3)^{2}$
  • ✓
    $(x+3)(x-3)$
  • D
    none of these
Answer
Correct option: C.
$(x+3)(x-3)$
c
$x^{2}-9=(x)^{2}-(3)^{2}=(x-3)(x+3)$
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MCQ 2131 Mark
The value of $\frac{0.73 \times 0.73 \times-0.27 \times 0.27}{0.73-0.27}$ is
  • ✓
    $1$
  • B
    $0$
  • C
    $0.73$
  • D
    $27$
Answer
Correct option: A.
$1$
Value $=\frac{(0.73+0.27)(0.73-0.27)}{0.73-0.27}=1$
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MCQ 2141 Mark
The factorisation of $\left(\frac{x^{2}}{y^{2}}-2+\frac{y^{2}}{x^{2}}\right) x \neq 0, y \neq 0$ is
  • A
    $\left(\frac{x}{y}+\frac{y}{x}\right)^{2}$
  • ✓
    $\left(\frac{x}{y}-\frac{y}{x}\right)^{2}$
  • C
    $\left(\frac{x}{y}-1\right)^{2}$
  • D
    $\left(\frac{x}{y}+1\right)^{2}$
Answer
Correct option: B.
$\left(\frac{x}{y}-\frac{y}{x}\right)^{2}$
b
$\frac{x^{2}}{y^{2}}-2+\frac{y^{2}}{x^{2}}$
$=\left(\frac{x}{y}\right)^{2}-2\left(\frac{x}{y}\right)\left(\frac{y}{x}\right)+\left(\frac{y}{x}\right)^{2}$
$=\left(\frac{x}{y}-\frac{y}{x}\right)^{2}$
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MCQ 2151 Mark
The value of $49^{2}$ is
  • ✓
    $(50)^{2}-2(50)(1)+(1)^{2}$
  • B
    $(50)^{2}+2(50)(1)+(1)^{2}$
  • C
    $(50)^{2}-(1)^{2}$
  • D
    $(\mathrm{d})(50)^{2}+(1)^{2}$
Answer
Correct option: A.
$(50)^{2}-2(50)(1)+(1)^{2}$
a
$49^{2}=(50-1)^{2}$
$=(50)^{2}-2(50)(1)+(1)^{2}$
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MCQ 2161 Mark
The value of $99^{2}$ is
  • ✓
    $(90)^{2}+2(90)(9)+(9)^{2}$
  • B
    $(90)^{2}-2(90)(9)+(9)^{2}$
  • C
    $(90)^{2}+(9)^{2}$
  • D
    none of these
Answer
Correct option: A.
$(90)^{2}+2(90)(9)+(9)^{2}$
a
$99^{2}=(90+9)^{2}$
$=(90)^{2}+2(90)(9)+(9)^{2}$
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MCQ 2171 Mark
The factorisation $x^{2}+x+\frac{1}{4}$ is
  • A
    $\left(\frac{x}{2}-1\right)^{2}$
  • B
    $\left(\frac{x}{2}+1\right)^{2}$
  • ✓
    $\left(x+\frac{1}{2}\right)^{2}$
  • D
    $\left(x-\frac{1}{2}\right)^{2}$
Answer
Correct option: C.
$\left(x+\frac{1}{2}\right)^{2}$
c
$x^{2}+x+\frac{1}{4}=x^{2}+2(x)\left(\frac{1}{2}\right)+\left(\frac{1}{2}\right)^{2}$
$=\left(x+\frac{1}{2}\right)^{2}$
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MCQ 2181 Mark
The factorisation $1+16 x+64 x^{2}$ is
  • A
    $(1-8 x)^{2}$
  • ✓
    $(1+8 x)^{2}$
  • C
    $(8-x)^{2}$
  • D
    $(8+x)^{2}$
Answer
Correct option: B.
$(1+8 x)^{2}$
b
$1+16 x+64 x^{2}$
$=(1) 2+2(1)(8 x)+(8 x)^{2}=(1+8 x)^{2}$
View full question & answer→
MCQ 2191 Mark
$0.645 \times 0.645+2 \times 0.645 \times 0.355+0.355 \times 0.355$ is
  • ✓
    $1$
  • B
    $0$
  • C
    $-1$
  • D
    $2$
Answer
Correct option: A.
$1$
Value $=(0.645+0.355)^{2}=(1)^{2}=1$
View full question & answer→
MCQ 2201 Mark
The factorisation of $(1+m)^{2}-4 \mid m$ is
  • ✓
    $(1-m)^{2}$
  • B
    $(1+m-2)^{2}$
  • C
    $(1+m+2)^{2}$
  • D
    none of these
Answer
Correct option: A.
$(1-m)^{2}$
a
$(1+m)^{2}-4 \ln$
$=\left.\right|^{2}+m^{2}+2 \operatorname{lm}-4 \mid m$
$=\left.\right|^{2}-2 \mid m+m^{2}=(\mid-m)^{2}$
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MCQ 2211 Mark
The factorisation of $(\mathrm{Im}+1)+\mathrm{m}+1$ is
  • ✓
    $(1+1)(m+1)$
  • B
    (6)$(1-1)(m-1)$
  • C
    $(1+1)(\mathrm{m}-1)$
  • D
    $(1-1)(m+1)$
Answer
Correct option: A.
$(1+1)(m+1)$
a
$|m+|+m+1$
$=\mid(m+1)+1(m+1)$
$=(1+1)(m+1)$
View full question & answer→
MCQ 2221 Mark
The factorisation of $\mathrm{am}^{2}+\mathrm{bm}^{2}+\mathrm{bn}^{2}+\mathrm{an}^{2}$ is
  • A
    $(a+b)\left(m^{2}-n^{2}\right)$
  • ✓
    $(a+b)\left(m^{2}+n^{2}\right)$
  • C
    $(a-b)\left(m^{2}+n^{2}\right)$
  • D
    $(a-b)\left(m^{2}-n^{2}\right)$
Answer
Correct option: B.
$(a+b)\left(m^{2}+n^{2}\right)$
b
$a m^{2}+b m^{2}+b n^{2}+a n^{2}$
$=m^{2}(a+b)+n^{2}(b+a)$
$=(a+b)\left(m^{2}+n^{2}\right)$
View full question & answer→
MCQ 2231 Mark
The factorisation of $z^{2}-4 z-12$ is
  • A
    $(z+6)(z+2)$
  • B
    $(z-6)(z-2)$
  • ✓
    $(z-6)(z+2)$
  • D
    $(z+6)(z-2)$
Answer
Correct option: C.
$(z-6)(z+2)$
c
$z^{3}-4 z-12$
$=z^{2}-6 z+2 z-12$
$=z(z-6)+2(z-6)$
$=(z-6)(z+2)$
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MCQ 2241 Mark
The factorisation of $y^{2}-7 y+12$ is
  • A
    $(y+3)(y+4)$
  • B
    $(y+3)(y-4)$
  • C
    $(y-3)(y+4)$
  • ✓
    $(y-3)(y-4)$
Answer
Correct option: D.
$(y-3)(y-4)$
d
$y^{2}-7 y+12$
$=y^{2}-3 y-4 y+12$
$=y(y-3)-4(y-3)$
$=(y-3)(y-4)$
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MCQ 2251 Mark
The factorisation of $4 \mathrm{y}^{2}-12 \mathrm{y}+9$ is
  • A
    $(2 y+3)^{2}$
  • ✓
    $(2 y-3)^{2}$
  • C
    $(3 y+2)^{2}$
  • D
    $(3 y-2)^{2}$
Answer
Correct option: B.
$(2 y-3)^{2}$
b
$4 y^{2}-12 y+9$
$=(2 y)^{2}-2(2 y)(3)+(3)^{2}$
$=(2 y-3)^{2}$
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MCQ 2261 Mark
The factorisation of $x^{2}+8 x+16$ is
  • A
    $(x+2)^{2}$
  • ✓
    $(x+4)^{2}$
  • C
    $(x-2)^{2}$
  • D
    $(x-A)^{2}$
Answer
Correct option: B.
$(x+4)^{2}$
b
$x^{2}+8 x+16$
$=(x)^{2}+2(x)(4)+(4)^{2}$
$=(x+4)^{2}$
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MCQ 2271 Mark
The factorisation of $x^{2} y^{2}+x y+x y^{2} z+y z+x^{2} y z+x z$ is
  • ✓
    $(x y+y z+z x)(x y+1)$
  • B
    $(x y+y z+z x)(y z+1)$
  • C
    $(x y+y z+z x)(z x+1)$
  • D
    none of these
Answer
Correct option: A.
$(x y+y z+z x)(x y+1)$
a
$x^{2} y^{2}+x y+x y^{2} z+y z+x^{2} y z+x z$
$=x y(x y+1)+y z(x y+1)+z x(x y+1)$
$=(x y+y z+z x)(x y+1)$
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MCQ 2281 Mark
The factorisation of$x^{2}+x+x y+y+z x+z$ is
  • ✓
    $(x+y+z)(x+1)$
  • B
    $(x+y+z)(x+y)$
  • C
    $(x+y+z)(y+z)$
  • D
    $(x+y+z)(z+x)$
Answer
Correct option: A.
$(x+y+z)(x+1)$
a
$x^{2}+x+x y+y+z x+z$
$=x(x+1)+y(x+1)+z(x+1)$
$=(x+1)(x+y+z)$
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MCQ 2291 Mark
The factorisation of $a b-a-b+1$ is
  • ✓
    $(a-1)(b-1)$
  • B
    $(a+1)(b+1)$
  • C
    $(a-1)(b+1)$
  • D
    $(a+1)(b-1)$
Answer
Correct option: A.
$(a-1)(b-1)$
a
$a b-a-b+1$
$=a(b-1)-1(b-1)$
$=(a-1)(b-1)$
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MCQ 2301 Mark
The factorisation of $a x+b x-a y-b y$ is
  • ✓
    $(x-y)(a+b)$
  • B
    $(x+y)(a+b)$
  • C
    $(x-y)(a-b)$
  • D
    $(x+y)(a-b)$
Answer
Correct option: A.
$(x-y)(a+b)$
a
$a x+b x-a y-b y$
$=x(a+b)-y(a+b)$
$=(x-y)(a+b)$
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MCQ 2311 Mark
The factorisation of $x^{2}+x y+2 x+2 y$ is
  • ✓
    $(x+2)(x+y)$
  • B
    $(x+2)(x-y)$
  • C
    $(x-2)(x+y)$
  • D
    $(x-2)(x-y)$
Answer
Correct option: A.
$(x+2)(x+y)$
a
$x^{2}+x y+2 x+2 y$
$=x(x+y)+2(x+y)$
$=(x+2)(x+y)$
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MCQ 2321 Mark
The factorisation of $6 x y-4 y+6-9 x$ is
  • ✓
    $(3 x-2)(2 y-3)$
  • B
    $(3 x+2)(2 y-3)$
  • C
    $(3 x-2)(2 y+3)$
  • D
    $(3 x+2)(2 y+3)$
Answer
Correct option: A.
$(3 x-2)(2 y-3)$
a
$6 x y-4 y+6-9 x$
$=2 y(3 x-2)-3(-2+3 x)$
$=(3 x-2)(2 y-3)$
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MCQ 2331 Mark
$a(x+y+z)+b(x+y+z)+c(x+y+z)$ is
  • ✓
    $(a+b+c)(x+y+z)$
  • B
    $(a b+b c+c a)(x+y+z)$
  • C
    $(x y+y z+z x)(a+b+c)$
  • D
    none of these
Answer
Correct option: A.
$(a+b+c)(x+y+z)$
a
$a(x+y+z)+b(x+y+z)+c(x+y+z)$
$=(x+y+z)(a+b+c)$
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MCQ 2341 Mark
The factorisation of $a x^{2} y+b x y^{2}+c x y z$ is
  • ✓
    $x y(a x+b y+c z)$
  • B
    $a x y(a x+b y+c z)$
  • C
    $b x y(a x+b y+c z)$
  • D
    $c x y(a x+b y+c z)$
Answer
Correct option: A.
$x y(a x+b y+c z)$
a
$a x^{2} y+b x y^{2}+c x y z=x y(a x+b y+c z)$
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MCQ 2351 Mark
The factorisation of $x^{2} y z+x y^{2} z+x y z^{2}$ is
  • ✓
    $x y z(x+y+z)$
  • B
    $x^{2} y z(x+y+z)$
  • C
    $x y^{2} z(x+y+z)$
  • D
    $x y z^{2}(x+y+z)$
Answer
Correct option: A.
$x y z(x+y+z)$
a
$x^{2} y z+x y^{2} z+x y z^{2}=x y z(x+y+z)$
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MCQ 2361 Mark
The factorisation of $a^{3}+a^{2} b+a b^{2}$ is
  • ✓
    $a\left(a^{2}+a b+b^{2}\right)$
  • B
    $6\left(a^{2}+a b+b^{2}\right)$
  • C
    $a b\left(a^{2}+a b+b^{2}\right)$
  • D
    rectangle
Answer
Correct option: A.
$a\left(a^{2}+a b+b^{2}\right)$
a
$a^{3}+a^{2} b+a b^{2}=a\left(a^{2}+a b+b^{2}\right)$
View full question & answer→
MCQ 2371 Mark
The factorisation of $28 a^{3} b^{5}-42 a^{5} b^{3}$ is
  • ✓
    $14 a^{3} b^{3}\left(2 b^{2}-3 a^{2}\right)$
  • B
    $14 a^{2} b^{3}\left(2 b^{2}-3 a^{2}\right)$
  • C
    $14 a^{3} b^{2}\left(2 b^{2}-3 a^{2}\right)$
  • D
    none of these
Answer
Correct option: A.
$14 a^{3} b^{3}\left(2 b^{2}-3 a^{2}\right)$
a
$28 a^{3} b^{5}-42 a^{5} b^{3}=14 a^{3} b^{3}\left(2 b^{2}-3 a^{2}\right)$
View full question & answer→
MCQ 2381 Mark
The factorisation of $6 x+12 y$ is
  • ✓
    $6(x+2 y)$
  • B
    $3(x+4 y)$
  • C
    $2(3 x+12 y)$
  • D
    none of these
Answer
Correct option: A.
$6(x+2 y)$
a
$6 x+12 y=6(x+2 y)$
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MCQ 2391 Mark
The factorisation of $6 x-42$ is
  • ✓
    $6(x-7)$
  • B
    $3(x-7)$
  • C
    $2(x-7)$
  • D
    24 cm
Answer
Correct option: A.
$6(x-7)$
a
$6 x-42=6(x-7)$
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MCQ 2401 Mark
The factorisation of $10 x^{2}-18 x^{3}+14 x^{4}$ is
  • ✓
    $2 x^{2}\left(7 x^{2}-9 x+5\right)$
  • B
    $2 x\left(7 x^{2}-9 x+5\right)$
  • C
    $2\left(7 x^{2}-9 x+5\right)$
  • D
    $2 x^{3}\left(7 x^{2}-9 x+5\right)$
Answer
Correct option: A.
$2 x^{2}\left(7 x^{2}-9 x+5\right)$
a$10 x^{2}-18 x^{3}+14 x^{3}=2 x^{2}\left(5-9 x+7 x^{2}\right)$
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MCQ 2411 Mark
The factorisation of $12 \mathrm{a}^{2} \mathrm{b}+15 \mathrm{ab}^{2}$ is
  • ✓
    $3 a b(4 a+5 b)$
  • B
    $3 a^{2} b(4 a+5 b)$
  • C
    $3 a b^{2}(4 a+5 b)$
  • D
    $3 a^{2} b^{2}(4 a+5 b)$
Answer
Correct option: A.
$3 a b(4 a+5 b)$
a
$12 a^{2} b+15 a b^{2}=3 a b(4 a+5 b)$
View full question & answer→
MCQ 2421 Mark
The common factor of $36 \mathrm{p}^{2} \mathrm{q}^{3} \mathrm{x}^{4}, 48 \mathrm{pq}^{3} \mathrm{x}^{2}$ and $54 \mathrm{p}^{3} \mathrm{q}^{3} \mathrm{x}^{4}$ is
  • ✓
    $6 \mathrm{pq}^{3} \mathrm{x}^{2}$
  • B
    $36 p q^{3} x^{2}$
  • C
    $54 \mathrm{pq}^{3} \mathrm{x}^{2}$
  • D
    $48 p q^{3} x^{2}$
Answer
Correct option: A.
$6 \mathrm{pq}^{3} \mathrm{x}^{2}$
a
$36 p^{2} q^{3} x^{4}=2 \times 2 \times 3 \times 3 \times p \times p \times q \times q \times q \times x \times x \times x \times x$
$48 p q^{3} x^{2}=2 \times 2 \times 2 \times 2 \times 3 \times p \times q \times q \times q \times x \times x$
$p^{3} q^{3} x^{4}=p \times p \times p \times q \times q \times q \times x \times x \times x \times x$
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MCQ 2431 Mark
The common factor of $72 x^{3} y^{4} z^{4}, 120 z^{2} d^{4} x^{4}$ and $96 y^{3} z^{4} d^{4}$ is
  • A
    $96 z^{3}$
  • B
    $120 z^{3}$
  • C
    $72 z^{3}$
  • ✓
    $24 z^{2}$
Answer
Correct option: D.
$24 z^{2}$
d
$72 x^{3} y^{4} z^{4}=2 \times 2 \times 2 \times 3 \times 3 \times x \times x \times x \times y \times y \times y \times y \times z \times z \times z \times z$
$120 z^{2} d^{4} x^{4}=2 \times 2 \times 2 \times 3 \times 5 \times z \times z \times d \times d \times d \times d \times x \times x \times x \times x$
$96 y^{3} z^{4} d^{4}=2 \times 2 \times 2 \times 2 \times 2 \times 3 \times y \times y \times z \times z \times z \times z \times d \times d \times d \times d$
View full question & answer→
MCQ 2441 Mark
The common factor of $24 x^{3} y^{4}, 36 x^{4} z^{4}$ and $48 x^{3} y^{2} z$ is
  • ✓
    $12 x^{3}$
  • B
    $24 x^{3}$
  • C
    $36 x^{3}$
  • D
    (d) $48 x^{3}$
Answer
Correct option: A.
$12 x^{3}$
a
$24 \mathrm{x}^{3} \mathrm{y}^{4}=2 \times 2 \times 2 \times 3 \times \mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{y} \times \mathrm{y} \times \mathrm{y} \times \mathrm{y}$
$36 \mathrm{x}^{4} \mathrm{z}^{4}=2 \times 2 \times 3 \times 3 \times \mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{z} \times \mathrm{z} \times \mathrm{z} \times \mathrm{z}$
$48 \mathrm{x}^{3} \mathrm{y}^{2} \mathrm{z}=2 \times 2 \times 2 \times 2 \times 3 \times \mathrm{x} \times \mathrm{x} \times \mathrm{x} \times \mathrm{y} \times \mathrm{y} \times \mathrm{z}$
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MCQ 2451 Mark
The common factor of $3 a^{2} b^{4} c^{2}, 12 b^{2} c^{4}$ and $15 a^{3} b^{4} c^{4}$ is
  • A
    $b^{4} c^{4}$
  • ✓
    $3 b^{2} c^{2}$
  • C
    $15 \mathrm{b}^{2} \mathrm{c}^{4}$
  • D
    $12 \mathrm{b}^{2} \mathrm{c}^{4}$
Answer
Correct option: B.
$3 b^{2} c^{2}$
b
$3 a^{2} b^{4} c^{2}=3 \times a \times a \times b \times b \times b \times b \times c \times c$ $12 b^{2} c^{4}=2 \times 2 \times 3 \times b \times b \times c \times c \times c \times c$ $15 a^{3} b^{4} c^{4}=3 \times 5 \times a \times a \times a \times b \times b \times b \times b \times c \times c \times c \times c$
View full question & answer→
MCQ 2461 Mark
The common factor of $2 a^{2} b^{4} c^{2}, 8 a^{4} b^{3} c^{4}$ and $6 a^{3} b^{4} c^{2}$ is
  • ✓
    $2 a^{2} b^{3} c^{2}$
  • B
    $6 a^{2} b^{3} c^{2}$
  • C
    $8 a^{2} b^{3} c^{2}$
  • D
    $a^{2}$
Answer
Correct option: A.
$2 a^{2} b^{3} c^{2}$
a
$6 a^{2} b^{4} c^{2}=2 \times a \times a \times b \times b \times b \times b \times c \times c \times c \times c$ $8 a^{4} b^{3} c^{4}=2 \times 2 \times 2 \times a \times a \times a \times a \times b \times b \times b \times c \times c \times c \times c$ $6 a^{3} b^{4} c^{2}=2 \times 3 \times a \times a \times a \times b \times b \times b \times b \times c \times c$
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MCQ 2471 Mark
The common factor of $6 a^{3} b^{4} c^{2}, 21 a^{2} b$ and $15 a^{3}$ is
  • ✓
    $3 a^{2}$
  • B
    $3 a^{3}$
  • C
    $6 a^{3}$
  • D
    $6 a^{2}$
Answer
Correct option: A.
$3 a^{2}$
a
$6 a^{3} b^{4} c^{2}=2 \times 3 \times a \times a \times a \times b \times b \times b \times b \times c \times c$ $21 a^{2} b=3 \times 7 \times a \times a \times a$ $15 a^{3} 64 c 4=3 \times 5 \times a \times a \times a$
View full question & answer→
MCQ 2481 Mark
The common factor of $8 a^{2} b^{4} c^{2}, 12 a^{4} b c^{4}$ and $20 a^{3} b^{4}$ is
  • A
    $a^{4} b^{4}$
  • B
    $a^{2} b^{2}$
  • C
    $4 a^{2} b^{2}$
  • ✓
    $4 a^{2} b$
Answer
Correct option: D.
$4 a^{2} b$
d
$8 a^{2} b^{4} c^{2}=2 \times 2 \times 2 \times a \times a \times b \times b \times b \times b \times c \times c$
$12 a^{4} b c^{2}=2 \times 2 \times 3 \times a \times a \times a \times a \times b \times c \times c$
$20 a^{3} b^{4}=2 \times 2 \times 5 \times a \times a \times a \times b \times b \times b \times b$
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MCQ 2491 Mark
The common factor of $14 \mathrm{a}^{2} \mathrm{b}$ and $35 \mathrm{a}^{4} \mathrm{b}^{2}$ is
  • A
    $a^{4} b^{2}$
  • B
    $35 a^{4} b^{2}$
  • C
    $14 a^{2} b$
  • ✓
    $7 a^{2} b$
Answer
Correct option: D.
$7 a^{2} b$
d
$14 a^{2} b=2 \times 7 \times a \times a \times b$
$35 a^{4} b^{2}=5 \times 7 \times a \times a \times a \times a \times b \times b$
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MCQ 2501 Mark
The common factor of $10ab, 30bc, 50ca$ is
  • ✓
    $10$
  • B
    $30$
  • C
    $50$
  • D
    $abc$
Answer
Correct option: A.
$10$
$10 a b=2 \times 5 \times a \times b$
$30 b c=2 \times 3 \times 5 \times b \times c$
$50 c a=2 \times 5 \times 5 \times c \times a$
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MCQ 2511 Mark
The common factor of $2 x, 3 x^{3}, 4$ is
  • ✓
    $1$
  • B
    $2$
  • C
    $3$
  • D
    $4$
Answer
Correct option: A.
$1$
$2 x=2 \times x$
$3 x^{3}=3 \times x \times x \times x$
$4=2 \times 2$
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MCQ 2521 Mark
The common factor $12y$ and $30$ is
  • ✓
    $6$
  • B
    $12$
  • C
    $30$
  • D
    $6y$
Answer
Correct option: A.
$6$
$12 y=2 \times 2 \times 3 \times y$
$30=2 \times 3 \times 5$
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MCQ 2531 Mark
The common factor of $\mathrm{p} 3 \mathrm{q} 4$ and $\mathrm{p} 4 \mathrm{q} 3$ is
  • A
    $\mathrm{p}^{4} \mathrm{q}^{4}$
  • B
    $p^{4} q^{3}$
  • ✓
    $p^{3} q^{3}$
  • D
    $p^{3} q^{4}$
Answer
Correct option: C.
$p^{3} q^{3}$
c
$p^{3} q^{4}=p \times p \times p \times q \times q \times q \times q$
$p^{4} q^{3}=p \times p \times p \times p \times q \times q \times q$
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MCQ 2541 Mark
The common factor of $\mathrm{a}^{2} \mathrm{m}^{4}$ and $\mathrm{a}^{4} \mathrm{m}^{2}$ is
  • A
    $a^{4} m^{4}$
  • ✓
    $a^{2} m^{2}$
  • C
    $a^{2} m^{4}$
  • D
    $a^{4} m^{2}$
Answer
Correct option: B.
$a^{2} m^{2}$
b
$a^{2} m^{4}=a \times a \times m \times m \times m \times m$
$a^{4} m^{2}=a \times a \times a \times a \times m \times m$
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MCQ 2551 Mark
The common factor of $x^{3} y^{2}$ and $x^{4} y$ is
  • A
    $x^{43} y^{2}$
  • B
    $x^{4} y$
  • C
    $x^{3} y^{2}$
  • ✓
    $4 a$
Answer
Correct option: D.
$4 a$
d
$x^{3} y^{2}=x \times x \times x \times y \times y$
$x^{4} y=x \times x \times x \times x \times y$
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MCQ 2561 Mark
The common factor of $x^{2} y^{2}$ and $x^{3} y^{3}$ is
  • ✓
    a
  • B
    $x^{3} y^{3}$
  • C
    $x^{2} y^{3}$
  • D
    $2 a b$
Answer
Correct option: A.
a
a
$x^{2} y^{2}=x \times x \times y \times y$
$x^{3} y^{3}=x \times x \times x \times y \times y \times y$
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