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
$4abc + 4ab^2c + 4abc^2$
AnswerCorrect 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.
$\Rightarrow\frac{9\times4\text{abc}(\text{a+b+c})}{9\text{abc}}$
$\Rightarrow4(\text{a+b+c})$
View full question & answer→MCQ 1521 Mark
The factorisation of $5x - 20$ is:
- A
$5(x - 5)$
- B
$5(x - 3)$
- ✓
$5(x - 4)$
- D
$5(x - 20)$
AnswerCorrect option: C. $5(x - 4)$
View full question & answer→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
$a(a + b + c)$
AnswerCorrect 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)$$
View full question & answer→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
$(x - 2)(x - y)$
AnswerCorrect option: A. $(x + 2)(x + y)$
A. $(x + 2)(x + y)$
Solution:
$= x^2 + xy + 2x + 2y$
$= x(x + y) + 2(x + y)$
$= (x + 2) (x + y)$
View full question & answer→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
$(1 + p) (1 - q) (1 - r)$
AnswerCorrect option: A. $(1 + p) (1 + q) (1 + r)$
$= 1 + p + q + r + pq + qr+pr + pqr$
$= 1 + p + q + pq + r(1 + p + q + pq)$
$= (1 + r) (1 + p + q + pq)$
$= (1 + r) (1 + p) (1 + q)$
View full question & answer→MCQ 1561 Mark
$105p^2q^2r^2\ (p + q)\ (q + r)\ (r + p) \div 21pq\ (q + r)\ (r + p)$
AnswerCorrect 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
$\Rightarrow5\text{pqr}^2(\text{p}+\text{q})$
View full question & answer→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
AnswerCorrect option: C. $2x + 3y = 2x + 3y$
$2x + 3y = 2x + 3y$
View full question & answer→MCQ 1581 Mark
One of the factors of $x^7 + xy^6$ is:
AnswerCorrect option: C. $x^2 + y^2$
C. $x^2 + y^2$
View full question & answer→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
AnswerCorrect option: A. $(l – m)^2$
A. $(l - m)^2$
Solution:
$= (1 + m)^2 - 4lm$
$= l^2 + m^2 + 2lm - 4lm$
$= l^2 - 2lm + m^2 = (l - m)^2$
View full question & answer→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
AnswerCorrect 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)$
View full question & answer→MCQ 1611 Mark
The common factor of $a^3b^2$ and $a^4b$ is:
- ✓
$a^3b$
- B
$a^4b^2$
- C
$a^4b$
- D
$a^3b^2$
AnswerCorrect option: A. $a^3b$
A. $a^3b$
Solution:
Same as question no. $11$
View full question & answer→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
$(3x - 4) (x + 2)$
AnswerCorrect option: A. $(3x + 4) (x + 2)$
A. $(3x + 4) (x + 2)$
Solution:
$= 3x^2 + 10x + 8 = 3x^2 + 6x + 4x + 8$
$= 3x(x + 2) + 4(x + 2)$
$= (x + 2) (3x + 4).$
View full question & answer→MCQ 1631 Mark
The factorisation $1 + 16x + 64x^2$ is:
- A
$(1 - 8x)^2$
- ✓
$(1 + 8x)^2$
- C
$(8 - x)^2$
- D
$(8 + x)^2$
AnswerCorrect option: B. $(1 + 8x)^2$
B. $(1 + 8x)^2$
Solution:
$1 + 16x + 64x^2$
$= (1)2 + 2(1) (8x) + (8x)^2 = (1 + 8x)^2$
View full question & answer→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
AnswerCorrect option: A. $(xy + yz + zx) (xy + 1)$
A. $(xy + yz + zx) (xy + 1)$
Solution:
$= x^2y^2 + xy + xy^2z + yz + x^2yz + xz$
$= xy(xy + 1) + yz(xy + 1) + zx(xy + 1)$
$= (xy + yz + zx) (xy + 1)$
View full question & answer→MCQ 1651 Mark
Which of the following is a factor of $m^4 - 256?$
- A
$m + 4$
- B
$m^2 + 4$
- C
$m^2 - 4$
- ✓
$m + 16$
AnswerCorrect option: D. $m + 16$
D. $m + 16$
View full question & answer→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
$9(m + 1) (m + 2)$
AnswerCorrect option: C. $3(m + 1) (m + 2)$
C. $3(m + 1) (m + 2)$
Solution:
$3m^2 + 9m + 6 = 3(m^2 + 3m + 2)$
$= 3 [m^2 + m + 2m + 2]$
$= 3 [m(m + 1) + 2( m + 1)]$
$= 3 [(m + 1) (m + 2)]$
View full question & answer→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
$(x + 4) (3x - 4)$
AnswerCorrect option: A. $(x - 4) (3x - 4)$
A. $(x - 4) (3x - 4)$
Solution:
$= 3x^2 - 16x + 16$
$= 3x^2 - 12x - 4x + 16$
$= 3x(x - 4) - 4(x - 4)$
$= (x - 4) (3x - 4)$
View full question & answer→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
$(1 + x) (1 + x)$
AnswerCorrect 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:
Answer$10a = 2 \times 5 \times a$
$20b = 2 \times 2 \times 5 \times b$
$30c = 2 \times 3 \times 5 \times c$
View full question & answer→MCQ 1701 Mark
Which of the following is quotient obtained on dividing $-18 xyz^2$ by $-3xz?$
- ✓
$6yz$
- B
$-6yz$
- C
$6xy^2$
- D
$6xy$
AnswerA. $6yz$
Solution:
$\frac{-18\text{xyz}^2}{-3\text{xz}}$
$\frac{-3\times6\times\text{z}\times\text{x}\times\text{z}}{-3\times\text{x}\times\text{z}}$
$=\frac{6\times\text{y}\times\text{z}}{1}$
$=6\text{yz}$
View full question & answer→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
AnswerCorrect option: A. $a(a^2 + ab + b^2)$
A. $a(a^2 + ab + b^2)$
Solution:
$a^2 + a^2b + ab^2 $
$= a(a^2 + ab + b^2)$
View full question & answer→MCQ 1721 Mark
The common factor of $14a^2b$ and $35a^4b^2$ is:
- A
$a^4b^2$
- B
$35a^4b^2$
- C
$14a^2b$
- ✓
$7a^2b$
AnswerCorrect 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 $40xyz?$
Answer$5xy = 5 \times 1 \times x \times y$
$3pqr = 3 \times 1 \times p \times q \times r$
$40xyz = 20 \times 2 \times 1 \times x \times y \times z$
Thus, the common factors are common factors of $1.$
View full question & answer→MCQ 1741 Mark
How many factors does $(x9 - x)$ have?
View full question & answer→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
$(1 + a - b)(1 - a + b)$
AnswerCorrect option: C. $(1 + a + b)(1 - a - b)$
C. $(1 + a + b)(1 - a - b)$
Solution:
$1 - 2ab - (a^2 + b^2)$
$= 1 - 2ab - a^2- b^2$
$= 1 - (a^2+ b^2 + 2ab)$
$= 1 - (a + b)^2$
$= (1 + a + b)(1 - a - b)$
View full question & answer→MCQ 1761 Mark
If $3x + 3y = 24$ and $2x - 3y = 12$ then the value of $xy$ is:
View full question & answer→MCQ 1771 Mark
On factorising $14pq + 35pqr$, we get:
- A
$pq(14 + 35r)$
- ✓
$7pq(2 + 5r)$
- C
$p(14q + 35qr)$
- D
$q(14p + 35pr)$
AnswerCorrect option: B. $7pq(2 + 5r)$
$= 14pq + 35pqr$
$= 2.7.p.q + 5.7.p.q.r$
$= 7pq(2 + 5r)$
View full question & answer→MCQ 1781 Mark
Which of the following is a factor of $6xy - 4y + 6 - 9x?$
- A
$2x + y$
- B
$x - y$
- C
$2x - 3$
- ✓
$3x - 2$
AnswerCorrect 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
$(7x^2 - 9x + 5)$
- ✓
$2x^2(7x^2 - 9x + 5)$
AnswerCorrect option: D. $2x^2(7x^2 - 9x + 5)$
D. $2x^2(7x^2 - 9x + 5)$
View full question & answer→MCQ 1801 Mark
$x^9 - x$ is having:
- A
$4$ factors.
- B
$2$ factors.
- ✓
$5$ factors.
- D
AnswerCorrect 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
$(x - 2) (x - 4)$
AnswerCorrect 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.
$= x^2 + 4x + 2x + 8$
$= x(x + 4) + 2(x + 4)$
$= x(x + 2) (x + 4)$
View full question & answer→MCQ 1821 Mark
Which of the following is a factor of $y^2 - 7y + 12?$
- A
$2y + 3$
- B
$y + 3$
- ✓
$y - 3$
- D
$2y - 2$
AnswerCorrect 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
$x^2 - y^2$
AnswerCorrect option: C. $y^2 - x^2$
C. $y^2 - x^2$
Solution:
$= (y - x) (y + x)$
$= y^2 - Xy + Xy - x^2$
$= y^2 - x^2$
View full question & answer→MCQ 1841 Mark
Sam is stuck at an equation $4a + a - 2a = 72$, help him find the value of a.
AnswerGiven equation is,
$4a + a - 2a = 72$
Solve the like terms.
$\Rightarrow 5a - 2a = 72$
$\Rightarrow 3a = 72$
$\Rightarrow a = 24$
View full question & answer→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
$(a + 1) (b - 1)$
AnswerCorrect option: A. $(a - 1) (b - 1)$
$= ab - a - b + 1$
$= a(b - 1) - 1(b - 1)$
$= (a - 1) (b - 1)$
View full question & answer→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
$5(11xz^2) + 9(11x^3z)$
AnswerCorrect 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 $11xz(5z + 9x^2).$
View full question & answer→MCQ 1871 Mark
What is the value of $2x - 3y + 4z$ at $x = 2, y = 0 \& z = 1$
View full question & answer→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
$(y + 2)(y - 3)$
AnswerCorrect option: B. $(y + 1)(y - 3)$
B. $(y - 1)(y + 3)$
Solution:
$y^2 + 2y - 3$
${-3 = 3 \times (-1), 2 = 3 - 1}$
$= y^2+ 3y - y - 3$
$= y(y + 3) - 1(y + 3)$
$= (y - 1)(y + 3)$
View full question & answer→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
$9(m+1)(m+2)$
AnswerCorrect option: B. $3(m+1)(m+2)$
b$3 m^{2}+9 m+6=3\left(m^{2}+3 m+2\right)$ $=3\left[m^{2}+m+2 m+2\right]$ $=3[m(m+1)+2(m+1)]$ $=3[(m+1)(m+2)]$
View full question & answer→MCQ 1901 Mark
When we factorise $x^{2}+5 x+6$, then we get:
AnswerCorrect 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 $a b=6$ $x^{2}+5 x+6=(x+2)(x+3)$
View full question & answer→MCQ 1911 Mark
The factors of $\mathrm{m}^{2}-256$ are:
- A
$(m+4)^{2}$
- B
$(m-4)^{2}$
- C
$(m-4)(m+4)$
- ✓
Answerd
$\mathrm{m}^{4}=\left(\mathrm{m}^{2}\right)^{2}$ and $256=(16)^{2}$
$\mathrm{m}^{4}-256=\left(\mathrm{m}^{2}\right)^{2}-(16)^{2}=\left(\mathrm{m}^{2}-16\right)\left(\mathrm{m}^{2}+16\right)$
$\mathrm{m}^{2}-16=\mathrm{m}^{2}-4^{2}=(\mathrm{m}-4)(\mathrm{m}+4)$
$\mathrm{m}^{4}-256=(\mathrm{m}-4)(\mathrm{m}+4)\left(\mathrm{m}^{2}+16\right)$
View full question & answer→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
AnswerCorrect option: C. $(7 p-6)(7 p+6)$
c
$49 p^{2}-36=(7 p)^{2}-(6)^{2}=(7 p-6)(7 p+6)$
View full question & answer→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
AnswerCorrect 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: $\left(\mathrm{a}-(\mathrm{b})^{2}=\mathrm{a}^{2}+\mathrm{b}^{2}-2 \mathrm{ab}\right.$
View full question & answer→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
$(x+y)(2 x+8)$
AnswerCorrect option: A. $(x+y)(x+8)$
a
$x^{2}+x y+8 x+8 y$
$=x(x+y)+8(x+y)$
$=(x+y)(x+8)$
View full question & answer→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
$(3 x+2)(2 y-3)$
AnswerCorrect option: B. $(3 x-2)(2 y-3)$
b
$6 x y-4 y+6-9 x$
$=6 x y-4 y-9 x+6$
$=2 y(3 x-2)-3(3 x-2)$
$=(3 x-2)(2 y-3)$
View full question & answer→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
$\mathrm{q}(14 \mathrm{p}+35 \mathrm{pr})$
- ✓
$7 \mathrm{pq}(2+5 \mathrm{r})$
AnswerCorrect option: D. $7 \mathrm{pq}(2+5 \mathrm{r})$
$14pq + 35pqr$
$=2.7 . p . q+5.7 . p . q . r$
$=7 \mathrm{pq}(2+5 r)$
View full question & answer→MCQ 1971 Mark
The factorisation of $12 x+36$ is
- ✓
$12(x+3)$
- B
$12(3 x)$
- C
$12(3 x+1)$
- D
$x(12+36 x)$
AnswerCorrect option: A. $12(x+3)$
a
$12 x+36$
$12 x+12.3$
$=12(x+3)$
View full question & answer→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
$3 a(4 a+5(b)$
- ✓
$3 b(4 a+5(b)$
AnswerCorrect 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 $3 a b$.
$12 a^{2} b+15 a b^{2}=3 a b(4 a+5 b)$
View full question & answer→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
$3 a b^{2}$
- ✓
$-3 a^{2} b^{2}$
AnswerCorrect option: D. $-3 a^{2} b^{2}$
View full question & answer→MCQ 2001 Mark
The quotient of $28 x^{2}+14 x$ is
Answer$\frac{28 x^{2} 1}{14 x}=\frac{2 \times 2 \times 7 \times x \times x}{2 \times 7 \times x}=2 \times$
View full question & answer→