Factorisation Questions

We provide factorisation practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on factorisation skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

Factorisation Questions

List of factorisation Questions

Question NoQuestionsClass
1Factorize :
( a^{4}+4 b^{4}+3 a^{2} b^{2} )
( mathbf{A} cdotleft(a^{2}+a+2 b^{2}right)left(a^{3}-a b+2 b^{3}right) )
B ( cdotleft(a^{2}-a b-2 b^{2}right)left(a^{2}-a b+2 b^{2}right) )
( mathbf{C} cdotleft(a^{3}+b+2 b^{3}right)left(a^{2}-a b+2 b^{2}right) )
D ( cdotleft(a^{2}+a b+2 b^{2}right)left(a^{2}-a b+2 b^{2}right) )
8
2State whether True or False:
Facatorization of ( 9 x^{2}-frac{1}{16} ) is ( (3 x- ) ( left.frac{1}{4}right)left(3 x+frac{1}{4}right) )
A. True
B. False
8
3Factors of ( 27-6 x-x^{2} ) are:
A . ( (3-x)(9+x) )
в. ( (x-3)(x+9) )
c. ( (x-2)(x+7) )
D. None of these
8
4Factorise ( boldsymbol{x} boldsymbol{y}left(boldsymbol{z}^{2}+mathbf{1}right)+boldsymbol{z}left(boldsymbol{x}^{2}+boldsymbol{y}^{2}right) )
A ( .(x y+z)(y z+x) )
B. ( (z x+y)(x y+z) )
c. ( (y z+x)(z x+y) )
D. ( left(x^{2}+y^{2}right)(z+x) )
8
5Factorize the following
( x^{2}+9 x-22 )
A. ( (x-2)(x+11) )
В. ( (x+2)(x+11) )
c. ( (x-2)(x-11) )
D. None of these
8
6Find the factors of the following expression:
( boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{x}+boldsymbol{a} boldsymbol{y}+boldsymbol{b} boldsymbol{y} )
This question has multiple correct options
( mathbf{A} cdot(a+b) )
в. ( (a-b) )
c. ( (x+y) )
D. ( (x-y) )
8
7Solve the following equations:
( (a+x)^{frac{2}{3}}+4(a-x)^{frac{2}{3}}=5left(a^{2}-x^{2}right)^{frac{1}{3}} )
8
8Divide the polynomial by monomial:
( y^{3}-64 ; y-4 )
( mathbf{A} cdot(y-4)left(y^{2}+4 y+16right)+0 )
B ( cdot(y+2)left(y^{2}+y+16right)+0 )
( mathbf{c} cdot(y+74)left(y^{2}-4 y+16right)+0 )
D. ( (y-3)left(y^{2}+3 y+2right)+0 )
8
9Factorise the expression: ( 7 p^{2}+21 q^{2} )
( mathbf{A} cdot 7left(p^{2}+q^{2}right) )
B. ( left(p^{2}-3 q^{2}right) )
C ( .7left(p^{2}+3 q^{2}right) )
D. ( left(p q^{2}+3 q^{2}right) )
8
10Factorise ( $ $ 5 x^{wedge} 2 y-15 x y^{wedge} 2 $ )
A ( .2 x y(2 x-15 y) )
в. ( 5 y(x-15 y) )
c. ( 5 x y(x-3 y) )
D. ( x y(5 x-3 y) )
8
11Factorise ( : 12 k y^{2}+8 k y-20 k )8
12Determine the value of ( p ) if ( (x+3) ) is a
factor of ( x^{3}-3 x^{2}-p x+24 )
8
13Factorise:
( boldsymbol{x}^{3}+mathbf{3} boldsymbol{x}^{2} boldsymbol{y}+mathbf{3} boldsymbol{x} boldsymbol{y}^{2}+boldsymbol{y}^{3}-mathbf{1 2 5}=mathbf{0} )
8
14Factorise ( 2 x^{2}-9 x+9 )8
15Find the prime factorisation of the following numbers:
( 85^{3}-68^{3}+5^{3}-22^{3} )
8
16Factorize: ( 3 a^{2} b-12 a^{2}-9 b+36 )8
17Factorise ( : 3 n^{2}-53 n+232 )8
18Simplify: ( left(a^{2} b^{2} c^{3}-a^{2} b^{2} c^{3}+a^{2} b^{2} c^{3}right) div )
( a^{2} b^{2} c^{3} )
( mathbf{A} cdot mathbf{1} )
B. –
( c )
D. None of these
8
19Factorise ( : 6 x y^{2}+4 x^{2} y )
A. ( 2 x y(3 x+y) )
B. ( x y(3 x+2 y) )
c. ( 2 x y(2 x+3 y) )
D. none of these
8
20Factorise: ( 4 sqrt{3} x^{2}+5 x-2 sqrt{3} )8
21The factors of ( 6-x-2 x^{2} ) are:
A. ( (x+2)(3-2 x) )
В. ( (3-x)(3 x+2) )
c. ( (x-2)(x+6) )
D. None of these
8
22Find the product of ( frac{k^{2}+13 k+42}{k^{2}+15 k+56} ) and ( frac{boldsymbol{k}^{2}+mathbf{8} boldsymbol{k}}{boldsymbol{k}^{2}+mathbf{1 1} boldsymbol{k}+mathbf{3 0}} )
A ( cdot frac{k^{2}+8 k}{k+5} )
в. ( frac{k}{k+5} )
c. ( frac{k}{k^{2}+15 k+56} )
D. ( frac{1}{k+5} )
8
23Find the remainder when ( x^{3}+3 x^{2}+ )
( 3 x+1 ) is divided by ( x+1 )
8
24Factorise the following expressions:
( boldsymbol{p}^{2}+boldsymbol{6} boldsymbol{p}+boldsymbol{8} )
A ( cdot(p-2)(p+4) )
в. ( (p+2)(p+4) )
c. ( (p+2)(p-4) )
D. ( (p-2)(p-4) )
8
25If a polynomial ( boldsymbol{f}(boldsymbol{x}) ) is divided by ( boldsymbol{x}^{2}- ) 16 then remainder is ( 5 x+3 ), what will
be the remainder when the same
polynomial is divided by ( (x+4) ? )
8
26Prove ( : boldsymbol{a}^{2}-boldsymbol{b}^{2}=(boldsymbol{a}+boldsymbol{b})(boldsymbol{a}-boldsymbol{b}) )8
27The remainder when ( x^{3}-2 x^{2}+4 x ) is
divided by ( x^{2} ) is
A .
в. ( x-2+frac{4}{x} )
c. ( 4 x )
D. ( 4 x-2 x^{2} )
8
28Factorise ( 4 a^{2}-8 a b )
A. ( 4 a(a+2 b) )
В. ( 4 a(a-b) )
c. ( 4 a(a-2 b) )
D. ( a(a-2 b) )
8
29Factorise ( (x-2 y)^{2}+7(x-2 y)+12 )8
30Factorise the expression and divide them as directed.
( left(5 p^{2}-25 p+20right) div(p-1) )
8
31Divide ( :left(51 m^{3} p^{2}-34 m^{2} p^{3}right) ) by ( 17 m p )
( mathbf{A} cdot m^{2} p )
В ( cdot m p^{2} )
c. ( 3 m^{2} p-2 m p^{2} )
D. ( m )
8
32Solve for ( r: )
( mathbf{4 1}=mathbf{4 0 0}left[left[frac{100+r}{100}right]^{2}-mathbf{1}right] )
8
33Factorise: ( 36 x^{2}+24 x+4 )
A. ( 4(3 x-1)(3 x+1) )
B. ( (3 x-1)(3 x+1) )
c. ( (3 x+1)(3 x+1) )
D. ( 4(3 x+1)(3 x+1) )
8
34Divide ( 15 x^{3}-20 x^{2}+13 x-12 ) by
( 3 x-6 )
8
35Divide the given polynomial by the given monomial:
( left(frac{2}{3} a^{2} b^{2} c^{2}+frac{4}{3} a b^{2} c^{2}right) div frac{1}{2} a b c )
A ( cdot frac{4}{3}(a b c+b c) )
в. ( frac{2}{3}(a b c+2 b c) )
c. ( frac{4}{3}(a b c+2 b c) )
D. None
8
36Factorize ( 3(y-2)^{2}-(y-2)-44 )8
37Simplify:
( 10 a^{2}-15 b^{2}+20 c^{2} )
A ( cdot 5left(2 a^{2}-3 b^{2}+4 c^{2}right) )
B. ( 5left(2 a-3 b^{2}+4 c^{2}right) )
C. ( 5left(10 a^{2}-3 b^{2}+4 c^{2}right) )
D. ( 5left(2 a^{2}+3 b^{2}+4 c^{2}right) )
8
38State whether True or False.
Factorization of ( a^{2}-16 b^{2}-2 a-8 b ) is
( (a+4 b)(a-4 b-2) )
A. True
B. False
8
39The value of ( left(9 x^{2}+18 x+27right) div 9 ) is
equal to
( mathbf{A} cdot x+2 )
B. ( x^{2}+2 x+2 )
c. ( x^{2}+2 x+3 )
D. ( x^{2}+2 x+1 )
8
40If ( 30 x^{3}+45 x^{2}-10 x ) is divided by ( 5 x )
find the resulting coefficient of ( x )
( A cdot 6 )
B. 9
c. 25
D. 40
8
41Factorization is the ( ldots ). process of
multiplication.
A. equal
B. same
c. inverse
D. common
8
42Find the remainder
( left(x^{2}+3 x+9right) div(x-3) )
8
43Factorize ( (boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{y})^{2}+(boldsymbol{b} boldsymbol{x}-boldsymbol{a} boldsymbol{y})^{2} ) by
the grouping method
A ( cdotleft(x^{2}+y^{2}right)left(a^{2}+b^{2}right) )
В – ( left(2 x^{2}+y^{2}right)left(a^{2}+b^{2}right) )
c. ( left(2 x^{2}+y^{2}right)left(2 a^{2}-b^{2}right) )
D. ( left(x^{2}+2 y^{2}right)left(a^{2}-b^{2}right) )
8
44If ( 0<x<y, ) then the positive square
root of ( boldsymbol{x}+boldsymbol{y}-boldsymbol{2} sqrt{boldsymbol{x} boldsymbol{y}} ) is
( mathbf{A} cdot sqrt{x}+sqrt{y} )
В. ( sqrt{x}-sqrt{y} )
c. ( sqrt{y}-sqrt{x} )
D. ( -sqrt{x}-sqrt{y} )
8
45Factorise the following:
( 2 x^{2}-7 x-15 )
A ( .(x+3)(x+4) )
В. ( (2 x+3)(x+5) )
c. ( (2 x+3)(x-5) )
D. ( (x-2)(x-8) )
8
46Factorise the following ( 9 x^{2}+6 x y+y^{2} )8
47Simplify: ( frac{boldsymbol{f}^{2}}{boldsymbol{g}}-boldsymbol{f} )
A. ( frac{f}{g}(f+g) )
в. ( fleft(frac{f}{g}+fright) )
c. ( quad f^{2}left(frac{1}{g}-frac{1}{f}right) )
D. ( f^{2}left(frac{1}{g}+1right) )
8
48If you factorise ( 4 p^{2}-(q+r)^{2} ) the
factors are
A ( cdot(2 p+q-r) )
в. ( (2 p-q-r) )
c. ( (2 p+q+r) )
D. Both B & C
8
49Divide ( 3 x^{4}+2 x^{2}-3 ) by ( (x+1) ) find
quotient and remainder
8
50Factorise: ( boldsymbol{x}^{2}-mathbf{3 6} )8
51Find the remainder using remainder
theorem, when:
( x^{3}-a x^{2}-5 x+2 a ) is divided by ( x-a )
8
52If ( alpha ) and ( beta ) are the roots of ( a x^{2}+b x+ )
( c=0, a neq 0 ) then the wrong statement
is
( ^{A} cdot alpha^{2}+beta^{2}=frac{b^{2}-2 a c}{a^{2}} )
B . ( alpha beta=frac{c}{a} )
( mathbf{c} cdot alpha+beta=frac{b}{a} )
D. ( frac{1}{alpha}+frac{1}{beta}=-frac{b}{c} )
8
53Factorize:
( 2 x^{3} b^{2}-4 x^{5} b^{4} )
8
54Factorise ( left(3-4 y-7 y^{2}right)^{2}-(4 y+1)^{2} )
A ( cdotleft(4-7 y^{2}right)left(2-8 y-7 y^{2}right) )
B ( cdotleft(7 y^{2}-4right)left(2-8 y-7 y^{2}right) )
c. ( left(4-7 y^{2}right)left(7 y^{2}+8 y-2right) )
D ( cdotleft(7 y^{2}-4right)left(7 y^{2}-8 y-2right) )
8
55Simplify ( x^{2}-2 x y+y^{2}=0 )8
56Which of the following should be added to ( 9 x^{3}+6 x^{2}+x+2 ) so that the sum is
divisible by ( (3 x+1) ? )
A . –
B . – –
( c cdot-2 )
D. –
8
57Divide the given polynomial by the given monomial
( 8left(x^{3} y^{2} z^{2}+x^{2} y^{3} z^{2}+x^{2} y^{2} z^{3}right) div )
( 4 x^{2} y^{2} z^{2} )
8
58Factorize the following expressions:
( mathbf{5} a^{2}+35 a )
8
59Factorise: ( boldsymbol{x}^{4}-mathbf{2} boldsymbol{x}^{2} boldsymbol{y}^{2}+boldsymbol{y}^{4} )8
60Determine whether ( (x+1) ) is a factor of
the polynomial:
( boldsymbol{x}^{3}-mathbf{1 4 x}^{mathbf{2}}+mathbf{3 x + 1 2} )
8
61State whether True or False
Factorization of ( x^{2}-y^{2}-2 y z-z^{2} ) is
( (x+y+z)(x-y-z) )
A. True
B. False
8
62Divide: ( left(-16 x^{6}-24 x^{4}right) ) by ( left(-8 x^{3}right) )
A ( cdot 2 x^{3}+3 x )
B ( .2 x^{2}+3 )
c. ( -2 x^{3}-3 x )
D. ( -2 x^{2}-3 )
8
63State whether True or False.
Factorization of ( 54 a^{2} b^{2}-6 ) is ( 6(3 a b+ )
1) ( (3 a b-1) )
A. True
B. False
8
64If ( x^{5}-9 x^{2}+12 x-14 ) is divisible by
( (x-3), ) what is the remainder?
( A cdot 0 )
B.
( c .56 )
D. 184
8
65Solve:
( 8 a^{2} b-3 a b+5 b^{2} b y 6 a b )
8
66Factorise: ( boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x}+mathbf{5}=mathbf{0} )8
67If ( (x+1) ) is a factor of ( x^{3}+11 x^{2}+15 x+ )
( a ) then the value of ‘a’ is
( A cdot 2 )
B. 3
( c cdot 5 )
D. 4
8
68Factorise ( boldsymbol{x}^{2}+boldsymbol{x}-mathbf{2} )8
69State whether True or False.
Factorization of ( (2 x-y)^{3}-(2 x-y) ) is
( (2 x-y)(2 x-y+1)(2 x-y-1) )
A. True
B. False
8
70Factorise:
( 4 x^{2}+9 y^{2}+25 z^{2}+12 x y+30 y z+ )
( 20 z x )
8
71Simplify: ( left(8 m^{2}-9 mright) div 3 m )
A ( cdot frac{1}{3}(8 m-9) )
B. ( 8 m-9 )
c. ( frac{1}{3}(8 m-3) )
D. ( 5 m-3 )
8
72Factorize:
( 3+2 a-a^{2} )
8
73If ( boldsymbol{x}=frac{boldsymbol{a}+boldsymbol{b}}{boldsymbol{a}-boldsymbol{b}} ) and ( boldsymbol{y}=frac{boldsymbol{a}-boldsymbol{b}}{boldsymbol{a}+boldsymbol{b}}, ) find ( boldsymbol{x}-boldsymbol{y} )8
74Find the value of a if ( 2 x^{3}-6 x^{2}+ )
( 5 a x-9 ) leaves the remainder 13 when it
is divided by ( x-2 )
8
75Solve :-
( left(3 x^{2}+5 x-9right) times(3 x-5) )
8
76Express the following as the product of exponent through prism factorization
( mathbf{1 1 5 6} )
8
77Factorize ( 25 m^{2}-70 m n+49 n^{2} )8
78Multiplying factors is an example of
A. polynomial
B. quadratic equation
c. division algorithm
D. factorisation
8
79Convert into factorials:
( mathbf{3} times mathbf{6} times mathbf{9} times mathbf{1 2} times mathbf{1 5} times mathbf{1 8} )
8
80Factorize the following
( x^{2}+13 x+30 )
A. ( (x+3)(x+10) )
в. ( (x-3)(x+10) )
c. ( (x+3)(x-10) )
D. None of these
8
81Factorise: ( 7 sqrt{2} y^{2}-10 y-4 sqrt{2} )8
82( left(14 x^{2} y z-28 x^{2} y^{2} z^{3}+32 y^{2} z^{2}right) div )
( (-4 x y) ) is equal to
A ( cdot frac{7}{2} y z+7 x y z^{2}+8 x y z )
B. ( -frac{7}{2} x z+7 x y z^{3}-frac{8 y z^{2}}{x} )
( ^{mathbf{C}}-frac{7}{2} x z-7 x y z^{3}+frac{8 y z^{2}}{x} )
D ( -frac{7}{2} x z-7 x y z^{2}-frac{8 y z^{2}}{x} )
8
83( left(49 x^{2} y z+35 pright) div 7 ) is equal to
A ( cdot 7 x^{2} y z-35 p )
B. ( 7 x^{2} y z+35 p )
c. ( 7 x^{2} y z-5 p )
D. ( 7 x^{2} y z+5 p )
8
84Factorise:
( x^{2}-6 x-135 )
( mathbf{A} cdot(5 x)(13 x+9) )
B. ( (x-15)(13 x+9) )
( mathbf{C} cdot(5 x)(x+9) )
D. ( (x-15)(x+9) )
8
85If ( f(x) ) and ( g(x) ) are two polynomials with integral coefficients which vanish at ( x=frac{1}{2}, ) then what is the factor of HCF
of ( boldsymbol{f}(boldsymbol{x}) ) and ( boldsymbol{g}(boldsymbol{x}) ? )
( mathbf{A} cdot x-1 )
B. ( x-2 )
c. ( 2 x-1 )
D. ( 2 x+1 )
8
86Factorise: ( boldsymbol{x}^{mathbf{4}}+boldsymbol{x}^{mathbf{2}}+mathbf{1} )8
87Factorise:
( y^{2}-5 y-24 )
8
88What is the remainder if ( boldsymbol{p}^{11}+boldsymbol{p}^{9}+ )
( p^{7}+p^{5}+p^{3}+p^{2} ) divided by ( p+1 )
8
89Find the value of ( a, ) if ( x-a ) is factor of
( boldsymbol{x}^{3}-boldsymbol{a}^{2} boldsymbol{x}+boldsymbol{x}+boldsymbol{2} )
8
90Evaluate: ( left(7 a^{2}-5 aright) div 5 a )
A ( .7 a-1 )
B. ( 7 a-5 )
c. ( frac{1}{5}(7 a-5) )
D. ( frac{1}{5}(7 a-1) )
8
91Divide: ( -4 x^{3}-6 x^{2}+8 x ) by ( 2 x )
A ( cdotleft(-2 x^{2}-3 x+4right) )
B. ( 2 xleft(2 x^{2}-3 x+4right) )
C ( cdotleft(-2 x^{2}-3 x+4right) )
D. ( xleft(-2 x^{2}-3 x-4right) )
8
92Write down all possible factors of ( 3 x^{2} y )8
93If ( alpha ) and ( beta ) are the roots of ( a x^{2}+b x+ )
( c=0, ) then the quadratic equation
whose roots are ( frac{1}{alpha} ) and ( frac{1}{beta} ) is
A ( cdot a x^{2}+b x+c=0 )
B. ( b x^{2}+a x+c=0 )
c. ( c x^{2}+b x+a=0 )
D. ( c x^{2}+a x+c=0 )
8
94Factorise ( boldsymbol{X}^{2}-mathbf{7} boldsymbol{X}+mathbf{1 0}=mathbf{0} )8
95Find the common factors of
( 3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z )
A ( cdot x^{2} y^{2} )
B. ( x y^{2} )
c. ( x^{2} y )
D. ( x y )
8
96f ( a+b+c=0 ), show that
( mathbf{6}left(boldsymbol{a}^{mathbf{5}}+boldsymbol{b}^{mathbf{5}}+boldsymbol{c}^{mathbf{5}}right)= )
( mathbf{5}left(boldsymbol{a}^{3}+boldsymbol{b}^{3}+boldsymbol{c}^{3}right)left(boldsymbol{a}^{2}+boldsymbol{b}^{2}+boldsymbol{c}^{2}right) )
8
97Factorise by using formula:
( left(7 frac{3}{10}right)^{2}-left(2 frac{1}{10}right)^{2} ) is ( 48 frac{22}{25} )
If true then enter 1 and if false then
enter 0
8
98Divide the given polynomial by the given monomial.
( left(p^{3} q^{6}-p^{6} q^{3}right) div p^{3} q^{3} )
8
99Factorize:
( x^{2}+14 x+33 )
8
100Determine whether ( (x+1) ) is a factor of
the polynomial:
( 6 x^{4}+7 x^{3}-5 x-4 )
8
101Which of the following expressions is the simplified form of the given
expression, given that ( m ) and ( n ) are positive? ( sqrt{9 m^{5} n^{2}-m^{4} n^{2}} )
A. ( 3 sqrt{m} )
в. ( 3 m n )
c. ( 3 n sqrt{m} )
D. ( m^{2} n sqrt{9 m-1} )
8
102Solve:
( x^{3}-x^{2}-14 x+14 )
8
103Factorise the expression: ( 10 a b+4 a+ )
( 5 b+2 )
A . ( (a+1)(5 b+1) )
B . ( (2 a-1)(5 b+1) )
c. ( (a+1)(b+10) )
D. ( (2 a+1)(5 b+2) )
8
104Simplify :-
( 2 x^{2}-x-3=0 )
8
105Simplify:
( boldsymbol{x}^{boldsymbol{6}}+boldsymbol{6} boldsymbol{x}^{boldsymbol{3}}+boldsymbol{8} )
8
106Factorize ( 16 x^{6}-8 x^{3} y^{3}+y^{6} ? )
A ( cdotleft(4 x^{3}-y^{3}right)^{2} )
B. ( left(4 x^{3}+y^{3}right)^{2} )
( mathbf{c} cdot(4 x+y)^{6} )
D. ( left(16 x^{2}+yright)^{2} )
8
107The denominator of an algebraic fraction should not be
A . 1
B. 0
( c cdot 4 )
( D )
8
108Factorize:
( boldsymbol{p q} boldsymbol{r}-boldsymbol{p}^{2} boldsymbol{q}+boldsymbol{p} boldsymbol{q}^{2} boldsymbol{r} )
8
109Solve using factorization method:
( mathbf{7} boldsymbol{m}^{2}-mathbf{8} mathbf{4}=mathbf{0} )
8
110Factories ( : 2 x y+2 y+3 x+3 )8
111( 7+3 x ) is a factor of ( 3 x^{3}+7 x )
A. True
B. False
8
112Factorise:
( 2 x^{2}-9 x+9 )
8
113Express in standard form ( (x-a)(x-b) )8
114( left(14 x^{2} y z-28 x^{2} y^{2} z^{3}+32 y^{2} z^{2}right) div )
( (-4 x y) )
A. ( frac{7}{2} y z+7 x y z^{2}+8 x y z )
B. ( -frac{7}{2} x z+7 x y z^{3}-frac{8 y z^{2}}{x} )
c. ( -frac{7}{2} x z-7 x y z^{3}+frac{8 y z^{2}}{x} )
D. ( frac{7}{2} x z-7 x y z^{2}-frac{8 y z^{2}}{x} )
8
115Factorize by the grouping method:
( 16(a+b)^{2}-4 a-4 b )
A ( .4(a-3 b)(4 a+4 b-1) )
B . ( 4(2 a+b)(a+4 b-3) )
c. ( 4(a-b)(4 a-4 b-1) )
D. ( 4(a+b)(4 a+4 b-1) )
8
116Prove that ( (boldsymbol{a}+boldsymbol{b})^{5}-boldsymbol{a}^{5}-boldsymbol{b}^{5}= )
( boldsymbol{5} boldsymbol{a b}(boldsymbol{a}+boldsymbol{b})left(boldsymbol{a}^{2}+boldsymbol{a} boldsymbol{b}+boldsymbol{b}^{2}right) )
8
117Simplify:
( 4 x^{2}-4 x z+6 y z-9 y^{2} )
8
118Factories ( : boldsymbol{p}^{2}+mathbf{6} boldsymbol{p}+mathbf{8} )8
119Factors of ( 16 x^{5}-144 x^{3} ) are
This question has multiple correct options
( mathbf{A} cdot 16 x^{3} )
B. 4
c. ( x+3 )
D. ( x-3 )
8
120Factorize the following ( 2 x^{2}-15 x+27 )8
121Divide ( left(9 x^{2}-24 x+16right) ) by ( (3 x-4) )
A ( .3 x-4 )
B. ( 4 x-3 )
c. ( (3 x-4)(3 x-4) )
D. ( 9 x^{2}-16 )
8
122Factorize ( : frac{36 m^{2}}{289}-81 )8
123Work out the following divisions:
( left(5 x^{3}-4 x^{2}+3 xright) div(2 x) )
8
124Find the value of
( (b-c)(c-a)(a-b)+ )
( (b-omega c)(c-omega a)(a-omega b)+ )
( left(b-omega^{2} cright)left(c-omega^{2} aright)left(a-omega^{2} bright) )
8
125Factorize using identities
( t^{4}-625 )
8
126Divide ( :-24 x^{2} y^{2}-4 x y ) by ( 2 x y )8
127Simplify : ( frac{boldsymbol{a}^{3}-mathbf{2 7}}{mathbf{5 a}^{2}-mathbf{1 6 a}+mathbf{3}} div )
( frac{boldsymbol{a}^{2}+mathbf{3} boldsymbol{a}+mathbf{9}}{mathbf{2 5 a}^{2}-mathbf{1}} )
8
128Factorise:
( 6 x yleft(a^{2}+b^{2}right)+8 y zleft(a^{2}+b^{2}right)- )
( mathbf{1 0 x z}left(mathbf{a}^{2}+mathbf{b}^{mathbf{2}}right) )
8
129( left(25 x^{5}-15 x^{4}right) div 5 x^{3} )
A. ( x(5 x+3) )
в. ( (5 x-3) )
c. ( x(5 x-3) )
D. None
8
130( 3 x^{2}-x-4 )8
131simplify ( : a^{3}-12 a-16 )8
132Factorize:
( 169 p^{2}-625 q^{2} )
8
133If area of a triangle is ( left(frac{4 x^{2}+8 x+4}{2}right) ) sq.units. Find its base and height8
134Factorise:
( (i) 25-4 x^{2}-12 x y-9 y^{2} )
( (i i) x^{2}-a^{2}+10 a b-25 b^{2} )
( (i i i) 6 x y+x^{2}+9 y^{2}-4 a^{2} )
( (i v) 9 x^{2}+4+12 x-a^{2}+2 a b-b^{2} )
8
135Factorise the following expressions:
( boldsymbol{x} boldsymbol{y}-boldsymbol{a b}(boldsymbol{x}+boldsymbol{y})+boldsymbol{a}^{2} boldsymbol{b}^{2} )
8
136Factorize the following
( 5 y^{2}-29 y+20 )
A. ( (5 y-4)(y-5) )
B. ( (5 y+4)(y-5) )
c. ( (5 y-4)(y+5) )
D. None of these
8
137Factorise:
( 9 x^{2} y^{2}-16 )
8
138Factorise the polynomial ( x^{2}-frac{1}{x^{2}} )8
139Which of the following is factorization of ( left(-56 m n p^{2}+7 m n pright) )
A. ( 7 m n p(-8 p+1) )
в. ( 7 m n p(8 p+1) )
( mathrm{c} .7 m n p(8 p-1) )
D. None of these
8
140Divide :
( 2 x^{3}-5 x^{2}-3 x b y(x-1) ? )
8
141If the polynomial ( f(x) ) is such that ( f(-43)=0, ) which of the following is
the factor of ( boldsymbol{f}(boldsymbol{x}) ) ?
A . ( x-43 )
B.
c. ( x-7 )
D. ( x+43 )
8
142Factorise :
( 121 a c-16 a^{2} b^{2} )
A ( cdot aleft(121 c-16 a b^{2}right) )
В . ( aleft(121 c+16 a b^{2}right) )
( mathbf{c} cdot aleft(121 c-16 a c^{2}right) )
D. none of these
8
143Factorise ( a^{2}(b+c)-(b+c)^{3} )
A ( cdot(b+c)left(a^{2}-(b+c)^{2}right. )
В ( cdot(b-c)left(a^{2}-(b+c)^{2}right. )
c. ( (b+c)left(a^{2}+(b+c)^{2}right) )
D. None of these
8
144The value of ( k ) for which ( x-1 ) is a
factor of the polynomial ( 4 x^{3}+3 x^{2}- )
( 4 x+k ) is
( A cdot 3 )
B.
( c cdot 1 )
D. – 3
8
145Factorize:
( 99 x^{2}-202 x y+99 y^{2} )
8
146Factorise the following:
( 3left(x^{2}-5 xright)^{2}-2left(x^{2}-5 x+5right)-6 )
A ( cdotleft(x^{2}-5 x+2right)left(3 x^{2}-5 x-8right) )
B. ( left(x^{2}-5 x+2right)left(3 x^{2}-15 x-8right) )
C. ( left(x^{2}-5 x-2right)left(3 x^{2}-15 x+8right) )
D. ( left(x^{2}-5 x-2right)left(3 x^{2}-5 x+8right) )
8
147Solve the following ( left(6 x^{4}+4 x^{2}+9 x+5right) div(2 x+3) )8
148Factorise the following:
( x^{2}+8 x+24 y-9 y^{2} )
A ( .(x+y)(x-3 y+8) )
в. ( (x+3 y)(x-3 y+8) )
c. ( (x+2 y)(x-3 y+8) )
D. ( (2 x+3 y)(x-3 y+8) )
8
149Factorise ( : boldsymbol{x}^{2}+mathbf{4} boldsymbol{x}+mathbf{3} )8
150Factorize:
( left(2 x^{3}+54right) )
8
151Simplify:
( left(1+frac{x^{2}-y^{2}-z^{2}}{2 y z}right)left(frac{1}{x+y-z}+frac{1}{z+}right. )
8
152Simplify: ( left(-80 m^{4} n p qright) div 10 m^{3} p q n^{2} )
( mathbf{A} cdot-8 m n )
в. -8 тпр( q )
( c .-8 m )
D. ( frac{-8 m}{n} )
8
153is a method of writing
numbers as the product of their factors or divisors.
A. Polynomial
B. Factorisation
c. Division algorithm
D. Quadratic equation
8
154Find integers ‘a’ and ‘b’ such that ( left(x^{2}-right. ) ( x-1) ) divides ( a x^{17}+b x^{16}+1 )8
155Evaluate ( left(x^{3}+2 x^{2}+3 xright) div 2 x )
A ( cdotleft(x^{2}+2 x-3right) div 2 )
B. ( left(x^{2}-2 x+3right) div 2 )
c. ( left(x^{2}+2 x+3right) div 2 )
D. ( left(x^{2}+x+3right) div 2 )
8
156Factorize the following
( x^{2}-2 x-99 )
A. ( (x+9)(x-11) )
В. ( (x-9)(x-11) )
c. ( (x+9)(x+11) )
D. None of these
8
157Factors of ( 8 x^{2}-18 x+9 ) are :
A. ( (4 x-3) ) and ( (2 x+3) )
B. ( (8 x-1) ) and ( (x-9) )
c. ( (8 x-3) ) and ( (x-3) )
D. ( (2 x-3) ) and ( (4 x-3) )
8
158Factorize ( 4 x^{2}-3 x-7 )8
159If ( 4 x^{4}-12 x^{3}+x^{2}+3 a x-b ) is divided
by ( x^{2}-1 ) then ( a=-1 )
( b= )
( mathbf{A} cdot 5,4 )
в. 4,9
( c cdot 4,5 )
D. 1,-1
8
160Factorise the given polynomial:
( 4 a^{2}-12 a b+9 b^{2}+4 a-6 b )
A. ( (2 a-3 b)(2 a-3 b+2) )
B. ( (2 a+3 b)(2 a-3 b+2) )
c. ( (2 a-3 b)(2 a+3 b-2) )
D. ( (2 a+3 b)(2 a-3 b-2) )
8
161Simplify :
( 3 x(2+5 x)-6(1-2 x) )
8
162Find the remainder using remainder theorem, when:
( 2 x^{3}-4 x^{2}+7 x+6 ) is divided by ( x-2 )
8
163Factorize the following expression ( 9 x^{2}+y^{2}+1-6 x y+6 x-2 y )
A ( cdot(3 x-y+1)^{2} )
в. ( (3 x-y+1)^{3} )
c. ( (3 x-y-1)^{2} )
D. None of these
8
164write the quotient and the remainder
( left(2 x^{4}+3 x^{3}+4 x-2right) div(x+2) )
8
165Solve: ( boldsymbol{x}(boldsymbol{3} boldsymbol{x}+mathbf{1 4})+boldsymbol{8} )
A ( cdot(x+4)(3 x+2) )
в. ( (x+2)(x+4) )
c. ( (x-4)(x+6) )
D. ( (x-2)(4 x+5) )
8
166The factors of ( 63 x^{2}-448 ) is
A. ( 9(7 x+8)(7 x-8) )
B. ( 7(3 x+8)^{2} )
c. ( 7(3 x+8)(3 x-8) )
D. ( 9(7 x-8)^{2} )
8
167If ( P(-7)=0 ) then a factor of ( P(x) ) is
( mathbf{A} cdot x-1 )
B. ( x+1 )
c. ( x+7 )
D. ( x-7 )
8
168Factorise the following expressions:
( a x^{2} y+b x y^{2}+c x y z )
A. ( x y(a x+b y+c z) )
B. ( operatorname{axy}(x+b y+c z) )
( c cdot b x y(a x+y+c z) )
D. ( x y(a x+b y-c z) )
8
169Factors of ( boldsymbol{x}^{boldsymbol{4}}-(boldsymbol{y}+boldsymbol{z})^{boldsymbol{4}} ) are
This question has multiple correct options
( mathbf{A} cdot(x-y-z) )
B.
( mathbf{c} cdot(x+y+z) )
D. ( left(x^{2}+y^{2}+z^{2}+2 y zright) )
8
170If the polynomial ( 3 x^{2}-x^{3}-3 x+5 ) is
divided by another polynomial ( boldsymbol{x}-mathbf{1}- )
( x^{2}, ) the remainder comes out to be 3
then quotient polynomial is
( mathbf{A} cdot 2-x )
B. ( 2 x-1 )
c. ( 3 x+4 )
D. ( x-2 )
8
171Factorise ( a-b-a^{2}+b^{2} )8
172Factorize ( : boldsymbol{y}^{2}+mathbf{1 0 0} boldsymbol{y} )
A. ( y(y+100) )
B . ( y^{2}(y+100) )
c. ( yleft(y^{2}+100right) )
D. none of these
8
173Factorise:
( 36 a^{2}+12 a b c-15 b^{2} c^{2} )
8
174If ( left(x+frac{1}{x}right)=6, ) fiind the vaue of
(i) ( left(x-frac{1}{x}right)(i i)left(x^{2}+frac{1}{x^{2}}right) )
8
175Factorize:
( boldsymbol{x}^{mathbf{1}}+boldsymbol{x}^{mathbf{2}} times mathbf{2} mathbf{5} )
8
176Factorize:
( 4 a^{2}-8 a b )
8
177Find ( (l+m)^{2}-(l-m)^{2} )
A ( .4 l m )
B. ( 2 l m )
( c cdot 0 )
( D )
8
178Factorize ( : 4 a x+4 a y )
A. ( 4 a(x+y) )
в. ( 4(x+y) )
c. ( 4 a(x-y) )
D. ( 4(x-y) )
8
179If ( f(x)=x^{3}+x^{2}-a x+b ) is divisible
by ( x^{2}-x ) write the value of a and ( b )
8
180Factorise:
( 4 x+12 )
( mathbf{A} cdot 4(x+2) )
B . ( 4(x+3) )
( mathbf{c} cdot 3(x+4) )
D. none of these
8
181Factorise: ( boldsymbol{x}^{4}-(boldsymbol{x}-mathbf{2})^{4} )8
182If ( (x-1) ) divides ( m x^{3}-2 x^{2}+25 x- )
26 with remainder ( 0, ) find the value of ( m )
8
183Determine ( p ) and ( q ) if ( p q=32 ) and ( p+ )
( boldsymbol{q}=-mathbf{1} mathbf{2} )
8
184Write the polynomial ( 3 x^{2}-5 x-2 ) as a
product of two first degree polynomials.
8
185Solve ( 16 a^{2}-40 a b+25 b^{2}-9 x^{2}+ )
( 42 x-49 )
8
186Factorise
( 2 a^{2}+10 a-28=0 )
8
187( left(3 x^{2}-2 xright) div x )
( A cdot 3 x )
B. ( 3 x-2 )
c. ( 3 x+2 )
D. None
8

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