MCQ

MCQ 11 Mark

Tick $(\checkmark)$ the correct answer: $x^3-144 x=?$

A
$x(x-12)^2$
B
$x(x+12)^2$
✓
$x(x-12)(x+12)$
D
None of these

Answer

Correct option: C.

$x(x-12)(x+12)$

$x^3-144 x$
$=x\left(x^2-144\right)$
$=x\left\{(x)^2-(12)^2\right\}$
$=x(x-12)(x+12)$

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MCQ 21 Mark

Tick $(\checkmark)$ the correct answer: $x^2-x z+x y-y z=?$

A
$(x-y)(x+z)$
B
$(x-y)(x-z)$
✓
$(x+y)(x-z)$
D
$(x-y)(z-x)$

Answer

Correct option: C.

$(x+y)(x-z)$

$x^2-x z+x y-y z$
$=x(x-z)+y(x-z)$
$=(x+y)(x-z)$

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MCQ 31 Mark

Tick $(\checkmark)$ the correct answer: $2 x^2+5 x+3=?$

A
$(x+3)(2 x+1)$
✓
$(x+1)(2 x+3)$
C
$(2 x+5)(x-3)$
D
None of these

Answer

Correct option: B.

$(x+1)(2 x+3)$

$2 x^2+5 x+3$
$=2 x^2+2 x+3 x+3$
$=2 x(x+1)+3(x+1)$
$=(2 x+3)(x+1)$

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MCQ 41 Mark

Tick $(\checkmark)$ the correct answer: $x^3-x=?$

A
$x\left(x^2-x\right)$
B
$x\left(x-x^2\right)$
C
$x(1+x)(1-x)$
✓
$x(x+1)(x-1)$

Answer

Correct option: D.

$x(x+1)(x-1)$

$x^3-x$
$=x\left(x^2-1\right)$
$=x(x-1)(x+1)$

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MCQ 51 Mark

Tick $(\checkmark)$ the correct answer: $\left(2 x-32 x^3\right)=?$

A
$2(x-4)(x+4)$
B
$2 x(1-2 x)^2$
C
$2 x(1+2 x)^2$
✓
$2 x(1-4 x)(1+4 x)$

Answer

Correct option: D.

$2 x(1-4 x)(1+4 x)$

$2 x-32 x^3=2 x\left(1-16 x^2\right)$
$=2 x\left\{(1)^2-(4 x)^2\right\}$
$=2 x(1-4 x)(1+4 x)$

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MCQ 61 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 71 Mark

Tick $(\checkmark)$ the correct answer: $x^2+4 x-21=?$

A
$(x-7)(x+3)$
✓
$(x+7)(x-3)$
C
$(x-7)(x-3)$
D
$(x+7)(x+3)$

Answer

Correct option: B.

$(x+7)(x-3)$

$x^2+4 x-21$
$=x^2+7 x-3 x-21$
$=x(x+7)-2(x+7)$
$=(x-3)(x+7)$

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MCQ 81 Mark

Tick $(\checkmark)$ the correct answer: $4 z^2-8 z+3=$ ?

✓
$(2 z-1)(2 z-3)$
B
$(2 z+1)(3-2 z)$
C
$(2 z+3)(3 z-1)$
D
$(z-1)(4 z-3)$

Answer

Correct option: A.

$(2 z-1)(2 z-3)$

$4 z^2-8 z+3$
$=4 z^2-6 z-2 z+3$
$\{4 \times 3=12,12=(-6) \times(-2),-8=-6-2\}$
$=2 z(2 z-3)-1(2 z-3)$
$=(2 z-1)(2 z-3)$

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MCQ 91 Mark

Tick $(\checkmark)$ the correct answer: $\left(12 m^2-27\right)=?$

A
$(2 m-3)(3 m-9)$
B
$3(2 m-9)(3 m-1)$
✓
$3(2 m-3)(2 m+3)$
D
None of these

Answer

Correct option: C.

$3(2 m-3)(2 m+3)$

$12 m^2-27$
$=3\left(4 m^2-9\right)$
$=3(2 m-3)(2 m+3)$

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MCQ 101 Mark

Tick $(\checkmark)$ the correct answer: $x^2+6 x+8=?$

A
$(x+3)(x+5)$
B
$(x+3)(x+4)$
✓
$(x+2)(x+4)$
D
$(x+1)(x+8)$

Answer

Correct option: C.

$(x+2)(x+4)$

$x^2+6 x+8$
$=x^2+4 x+2 x+8$
$\{8=4 \times 2,6=4+2\}$
$=x(x+4)+2(x+4)$
$=(x+2)(x+4)$

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MCQ 111 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 121 Mark

Tick $(\checkmark)$ the correct answer: $40+3 x-x^2=?$

A
$(x+5)(x-8)$
B
$(5-x)(8+x)$
✓
$(5+x)(8-x)$
D
$(5-x)(8-x)$

Answer

Correct option: C.

$(5+x)(8-x)$

$40+3 x-x^2$
$=40+8 x-5 x-x^2$
$\{40=8 x(-5), 3=8-5\}$
$=8(5+x)-x(5+x)$
$=(8-x)(x+5)$

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MCQ 131 Mark

Tick $(\checkmark)$ the correct answer: $3+23 y-8 y^2=?$

A
$(1-8 y)(3+y)$
✓
$(1+8 y)(3-y)$
C
$(1-8 y)(y-3)$
D
$(8 y-1)(y+3)$

Answer

Correct option: B.

$(1+8 y)(3-y)$

$3+23 y-8 y^2$
$=3+24 y-y-8 y^2$
$\{3 \times(-8)=-24,-24=24 \times(-1), 23=24-1\}$
$=3(1+8 y)-y(1+8 y)$
$=(1+8 y)(3-y)$

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MCQ 141 Mark

Tick $(\checkmark)$ the correct answer of the following: $\left(7 a^2-63 b^2\right)=$ ?

A
$(7 a-9 b)(9 a+7 b)$
B
$(7 a-9 b)(7 a+9 b)$
C
$9(a-3 b)(a+3 b)$
✓
$7(a-3 b)(a+3 b)$

Answer

Correct option: D.

$7(a-3 b)(a+3 b)$

$7 a^2-63 b^2=7\left(a^2-9 b^2\right)$
$=7\left\{(a)^2-(3 b)^2\right\}$
$=7(a-3 b)(a+36)$

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MCQ 151 Mark

Tick $(\checkmark)$ the correct answer: $\left(2-50 x^2\right)=?$

A
$2(1-5 x)^2$
B
$2(1+5 x)^2$
C
$(2-5 x)(2+5 x)$
✓
$2(1-5 x)(1+5 x)$

Answer

Correct option: D.

$2(1-5 x)(1+5 x)$

$2-50 x^2=2\left(1-25 x^2\right)$
$=2\left\{(1)^2-(5 x)^2\right\}$
$=2(1-5 x)(1+5 x)$

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MCQ 161 Mark

Tick $(\checkmark)$ the correct answer: $p q^2+q(p-1)-1=?$

A
$(p q+1)(q-1)$
B
$p(q+1)(q-1)$
C
$q(p-1)(q+1)$
✓
$(p q-1)(q+1)$

Answer

Correct option: D.

$(p q-1)(q+1)$

$p q^2+q(p-1)-1$
$=p q^2+p q-q-1$
$=p q(q+1)+-1(q+1)$
$=(q+1)(p q-1)$

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MCQ 171 Mark

Tick $(\checkmark)$ the correct answer: $a^2+b c+a b+a c=?$

✓
$(a+b)(a+c)$
B
$(a+b)(b+c)$
C
$(b+c)(c+a)$
D
$a(a+b+c)$

Answer

Correct option: A.

$(a+b)(a+c)$

$a^2+b c+a b+a c$
$=a^2+a b+a c+b c$
$=a(a+b)+c(a+b)$
$=(a+b)(a+c)$

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MCQ 181 Mark

Tick $(\checkmark)$ the correct answer: $1-2 a b-\left(a^2+b^2\right)=$ ?

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.

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

$1-2 a b-\left(a^2+b^2\right)$
$=1-2 a b-a^2-b^2$
$=1-\left(a^2+b^2+2 a b\right)$
$=1-(a+b)^2$
$=(1+a+b)(1-a-b)$

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MCQ 191 Mark

Tick $(\checkmark)$ the correct answer: $y^2+2 y-3=?$

✓
$(y-1)(y+3)$
B
$(y+1)(y-3)$
C
$(y-1)(y-3)$
D
$(y+2)(y-3)$

Answer

Correct option: A.

$(y-1)(y+3)$

$y^2+2 y-3$
$\{-3=3 \times(-1), 2=3-1\}$
$=y^2+3 y-y-3$
$=y(y+3)-1(y+3)$
$=(y-1)(y+3)$

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