CBSE Class 8 Mathematics Factorisation Assignment Set I

Question. The factors of x²/4 - y²/9 are ____.
(A) (x/4 + y/9) (x/4 - y/9)
(B) (x/2 + y/9) (x/2 - y/9)
(C) (x/2 + y/3) (x/2 - y/3)
(D) Both (A) and (B)
Answer : C

Question. The factors of 15x² – 26x + 8 are ____.
(A) (3x – 4) (5x + 2)
(B) (3x – 4) (5x – 2)
(C) (3x + 4) (5x – 2)
(D) (3x + 4) (5x + 2)
Answer : B

Question. One of the factors of (p + q)² – (a – b)² + p + q – a + b is
(A) (p + q + a + b)
(B) (p + q – a + b)
(C) (p – q + a – b)
(D) (p – q + a + b)
Answer : B

Question. If (x² + 3x + 5) (x² – 3x + 5) = m² – n², then m =____.
(A) x² – 3x
(B) 3x
(C) x² + 5
(D) Both (A) and (B)
Answer : C

Question. Which of the following is the factor of 12(a² + 7a)² – 8(a² + 7a)(²a – 1) – 15 (2a – 1)2 ?
(i) (2a² + 8a + 3) (ii) (6a² + 52a – 5)
(iii) (3a + 5)
(A) Only (i)
(B) Both (i) and (ii)
(C) Only (ii)
(D) All (i), (ii) and (iii)
Answer : B

Question. The factors of x² – 16 are ____.
(A) (x² + 2)(x² – 2)
(B) (x + 4)(x – 4)
(C) (x + 2)(x – 2)
(D) Does not exist
Answer : B

Question. The factors of √3x² + 11x + 6√3 are ____.
(A) (x − 3√3) (√3x + 2)
(B) (x − 3√3) (√3x − 2)
(C) (x + 3√3) (√3x − 2)
(D) (x + 3√3) (√3x + 2)
Answer : D

Question. Factorisation of xy – pq + qy – px is ____.
(A) (y – p) (x + q)
(B) (y – p) (x – q)
(C) (y + p) (x + q)
(D) (y + p) (x – q)
Answer : A

Question. The factors of x⁴ + y⁴ + x²y² are ____.
(A) (x² + y²)(x² + y² – xy)
(B) (x² + y²)(x² – y²)
(C) (x² + y² + xy) (x² + y² – xy)
(D) Factorisation is not possible
Answer : C

Question. For x² + 2x + 5 to be a factor of x⁴ + px² + q, the values of p and q must be ____.
(A) – 2, 5
(B) 5, 25
(C) 10, 20
(D) 6, 25
Answer : D

Question. One of the factors of 4(x + y)(3a – b) + 6 (x + y)(2b – 3a) is
(A) (2b – 3a)
(B) (3a – b)
(C) (4a – 3b)
(D) (– 3a + 4b)
Answer : D

Question. Divide (32x⁴y³ – 16x³y⁴) by (–8x²y)
(A) 4x³y² + 2xy³
(B) 4x³y – 2xy³
(C) – 4x²y² + 2xy³
(D) –4xy² + 2xy³
Answer : C

Question. Factorise: (2x + 3y)² – 5(2x + 3y) – 14.
(A) 4(2x + 3y)(x + y – 2)
(B) 4(2x + 3y)(x + y + 2)
(C) (2x – 3y + 7)(2x – 3y + 2)
(D) (2x + 3y – 7)(2x + 3y + 2)
Answer : D

Question. Simplify : −14x¹²y + 8x⁵z / 2x²
(A) x³(– 7x7y + 4z)
(B) x²(7x7y – 4z)
(C) x²(–7x6y + 2z)
(D) x³(7x7y + 4z)
Answer : A

Question. Do as directed.
(i) Factorise: x² + 1/x² − 3
(ii) Find the greatest common factors of 14x²y³, 21x³y² and 35x⁴y⁵z.
(iii) Divide z(5z² – 80) by 5z(z + 4).

Answer : C

Question. Fill in the blanks.

Answer : D

Question. Which of the following statements is CORRECT?
(A) The factors of an expression are always either algebraic variable or algebraic expression.
(B) An irreducible factor is a factor that cannot be expressed further as a product of factors.
(C) Every binomial expression can be factorised into two monomial expression.
(D) The process of writing a given expression as the product of two or more factors is called multiplication of factors.
Answer : B

Question. Match the expression given in Column-I to one of their factors given in Column-II.
         Column-I               Column-II
P. 9x² + 24x + 16           (i) (2x – 4)
Q. 25x² + 30x + 9          (ii) (4x + 1)
R. 40x² + 14x + 1          (iii) (5x + 3)
S. 4x² – 16x + 16          (iv) (3x + 4)
(A) P → (iv); Q → (iii); R → (ii); S → (i)
(B) P → (iii); Q → (i); R → (iv); S → (ii)
(C) P → (ii); Q → (i); R → (iv); S → (iii)
(D) P → (iv); Q → (iii); R → (i); S → (ii)
Answer : A

Question. Factors of x⁴ – (x – z)⁴ are ____.
(A) (2x + z)(2x³ + z³ – 2x²)
(B) z(x + 2z)(x² + z² – x²)
(C) z(2x – z)(2x² – 2xz + z²)
(D) z(x – 2z)(2z² – 2xz + x²)
Answer : C

Question. Factorising (x – y)² + 4xy – z², we get
(A) (x + y + z)(x + y – z)
(B) (x – y – z)(x + y – z)
(C) (x – y + z)(x + y – z)
(D) None of these
Answer : A

Question. Complete it : x² + 25x + 84 = (x + 21) × _______.
Answer : (x + 4)

Question. Find the product : (a – b – c) (a – b + c)
Answer : a² – 2ab + b² – c²

Question. Simplify : x² - 13x + 40 / (x - 8)
Answer : x – 5

Question. Find the value of 34 – 14 using the identity x⁴ – y⁴ = (x + y) (x – y) (x² + y²).
Answer : 80

Question. Express as product of two linear factors. x² – 17x + 16.
Answer : (x – 16) (x – 1)

Question. Find z if, (x + 4) (x – 5) – z = x(x – 1)
Answer : –20

Question. Factorize : x²(y + 5) –4(y + 5)
Answer : (y + 5) (x + 2) (x – 2)

Question. Divide 121x⁵y⁴z³ by 11x³y²z.
Answer : 11x²y²z²

Question. Find the common factor in 7x²y + 49xy² + 343x³y².
Answer : 7xy

Question. Factorize : x² – 3x + 2.
Answer : (x – 2) (x – 1)

Question. Find the value of  x³y xy³/xy as a product of two factors.
Answer : (x + y) (x – y).

Question. Complete it : (x + 3) (x – 5) = x² + ( )x + ( ).
Answer : –2, –15.

Question. Factorize : 16x² + 40xy + 25y²
Answer : (4x + 5y)²

Question. Simplify : (1.9)² - (1.1)² / 3
Answer : 0.8

Question. Find (x4 + y4) (x⁴ – y4) if x = 1, y = 1.
Answer : 0

Question. Find the value of 252 – 242.
Answer : 49

Question. Simplify : (0.87)² - (0.13)² / (0.87 - 0.13)
Answer : 1

Question. Find the quotient : z(4y² – 64) 4z(y – 4)
Answer : y + 4

Question. Find x and y that xy = 72, x + y = 17.
Answer : x = 9, y = 8.

Question. Simplify : 4m² - 169n² / 2m + 13n
Answer : 2m – 13n

Question. Find the value of : (3a + b)² – (3a – b)².
Answer : 12ab
 

Q 1 Factorise 2x + 4.

Q 2 Factorise 12a²b + 15ab².

Q 3 Factorise 10x² – 14x3 + 18x⁴

Q 4 Factorise 20x²y + 30axy.

Q 5 Factorise x² + xy + 8x + 8y.

Q 6 Factorise 1 + a + ac + a²c.

Q 7 Factorise a² + bc + ab + ac.

Q 8 Factorise x² – 36 using identity.

Q 9 Factorise xy – pq + qy – px.

Q 10 Factorise 5a(2x – 3y) + 2b(2x - 3y).

Q 11 Factorise ax² + by² + bx² + ay².

Q 12 Factorise 8(4x + 5y)² – 12(4x + 5y).

Q 13 Factorise using identity x² + 10x + 25.

Q 14 Factorise using identity 4x² + 9y² + 12xy.

Q 15 Factorise ax²y + bxy² + cxyz.

Questions carrying 1 mark each :-

Q.1 Factorise x² + x.

Q.2 Is it correct : 3(x-4) = 3x -4.

Questions carrying 2 marks each :-

Q.3 Factorise 9a² - 16b²

Q.4 Factorise 24x⁴ + 18x³

Q.5 Factorise 2a - 32a⁵

Q.6 Evaluate(ax+ay+ax) a

Questions carrying 3 marks each :

Q.7 Factorise 1-a² - 2ab - b²

Q.8 Resolve into factors : 2x² - 3ax - 2a²

Q.9 Find the greatest common factor of - 4a³b², 12a³b³c, 16a⁵bc.

Q.10 Divide (4x²-9) by (2x-3).

Q.11 Factorise (x⁴) - (y-z)⁴

Multiple Choice Questions carrying 1mark each:-

Q.12 Division is opposite of

a) Subtraction

b) Addition

c) Multiplication

d) None of these

Multiple Choice Questions carrying 1mark each:-

Q.13 Division is opposite of
a) Subtraction
b) Addition
c) Multiplication
d) None of these