MCQs on Class 8 Factorisation
MULTIPLE CHOICE QUESTIONS
1. The factorisation of 12a2b+15ab2 gives:
A. 3ab(4ab+5)
B. 3ab(4a+5b)
C. 3a(4a+5b)
D. 3b(4a + 5b)
Answer: B
Explanation: 12a2b+15ab2
12a2b = 3 x 4 x a x a x b
15ab2 = 3 x 5 x a x b x b
The common factors are 3ab.
12a2b+15ab2 = 3ab(4a+5b)
2. The factorisation of 12x+36 is
A. 12(x+3)
B. 12(3x)
C. 12(3x+1)
D. x(12+36x)
Answer: A
Explanation: 12x + 36
12 x + 12 . 3
=12(x+3)
3. On factorising 14pq + 35pqr, we get:
A. pq(14+35r)
B. p(14q+35qr)
C. q(14p+35pr)
D. 7pq(2+5r)
Answer: D
Explanation: 14pq + 35pqr
= 2.7.p.q + 5.7.p.q.r
= 7pq(2+5r)
4. The factors of 6xy – 4y + 6 – 9x are:
A. (3x + 2) (2y + 3)
B. (3x – 2) (2y – 3)
C. (3x – 2) (2y + 3)
D. (3x –+2) (2y – 3)
Answer: B
Explanation: 6xy – 4y + 6 – 9x
= 6xy – 4y – 9x + 6
= 2y (3x – 2) – 3 (3x – 2)
= (3x – 2) (2y – 3)
5. The factors of x2+xy+8x+8y are:
A. (x+y) (x+8)
B. (2x+y) (x+8)
C. (x+2y) (x+8)
D. (x+y) (2x+8)
Answer: A
Explanation: x2+xy+8x+8y
= x(x+y)+8(x+y)
=(x+y)(x+8)
6. The factors of 4y2 – 12y + 9 is:
A. (2y+3)2
B. (2y-3)2
C. (2y-3)(2y+3)
D. None of the above
Answer: B
Explanation: 4y2 – 12y + 9
4y2 = (2y)2 & 9 = 32 & 12y = 2.3.2y
4y2 – 12y + 9 = (2y)2 – 2 × 3 × (2y) + (3)2
= (2y – 3)2 [By algebraic identities: (a-b)2 = a2+b2-2ab
7. The factors of 49p2 – 36 are:
A. (7p+6)2
B. (7p-6)2
C. (7p – 6 ) ( 7p + 6)
D. None of the above
Answer: C
Explanation: 49p2 – 36 = (7p)2 – ( 6 )2 = (7p – 6 ) ( 7p + 6)
8. The factors of m2 – 256 are:
A. (m + 4)2
B. (m – 4)2
C. (m – 4) (m+4)
D. None of the above
Answer: D
Explanation: m2 = (m)2 and 256 = (16)2
By using the algebraic identity, a2-b2 = (a+b).(a-b), we get (m+16).(m-16).
9. When we factorise x2+5x+6, then we get:
A. (x +2) (x + 3)
B. (x – 2) (x – 3)
C. (x × 2) + (x × 3)
D. (x × 2) – (x × 3)
Answer: A
Explanation: The factors of a form:
(x + a) (x + b) = x2 + (a + b) x + ab
x2+5x+6
a+b = 5 and ab = 6
x2+5x+6 = (x +2) (x + 3)
10. The factors of 3m2 + 9m + 6 are:
A. (m + 1) (m + 2)
B. 3(m + 1) (m + 2)
C. 6(m + 1) (m + 2)
D. 9(m + 1) (m + 2)
Answer: B
Explanation: 3m2 + 9m + 6 = 3(m2 + 3m + 2)
= 3 [m2 + m + 2m + 2]
= 3 [m(m + 1)+ 2( m + 1)]
= 3 [(m + 1) (m + 2)]
11. The common factor of a3b3 and ab2 is:
A. a2b2
B. ab2
C. a2b
D. ab
Answer: B. ab2
a3b3 = a x a x a x b x b x b
ab2 = a x b x b
The common factors are: a × b × b = ab2
12. The common factor of a3b2 and a4b is:
A. a4b2
B. a4b
C. a3b2
D. a3b
Answer: D. a3b
Explanation: Same as question no.11
13. The common factor 12a and 30 is:
A.6
B. 12
C. 30
D. 6a
Answer: A.
12a = 2 x 2 x 3 x a
30 = 2 x 3 x 5
14. The common factors of 10a, 20b and 30c are:
A. ab
B. ac
C. 10abc
D. 10
Answer: 10
10a = 2 x 5 x a
20b = 2 x 2 x 5 x b
30c = 2 x 3 x 5 x c
15. The common factor of 6x3y4z2, 21x2y and 15x3 is:
A. 3x2
B. 3x3
C. 6x3
D. 6x2
Answer: A. 3x2
Explanation: Same as question number 14.
16. The common factor of 24a3b4, 36a4c4 and 48a3b2c is:
A. 12a3
B. 24a3
C. 36a3
D. 48a3
Answer: A. 12a3
Explanation:
24a³b4 = 2 × 2 × 2 × 3 × a × a × a × b × b × b × b
36a4c4 = 2 × 2 × 3 × 3 × a × a × a × a × c × c × c × c
48a3b2c = 2 × 2 × 2 × 2 × 3 × a × a × a × b × b × c
17. The factorisation of 12x2y + 15xy2 is:
A. 3xy2 (4x + 5y)
B. 3x2y (4x + 5y)
C. 3xy (4x + 5y)
D. 3x2y2 (4x + 5x)
Answer: C. 3xy (4x + 5y)
12x2y + 15xy2 = 3xy (4x + 5y)
18. The factorisation of 5x – 20 is:
A. 5(x-5)
B. 5(x-4)
C. 5(x-3)
D. 5(x-20)
Answer: B. 5(x-4)
Explanation: 5x – 20 = 5 (x – 4)
19. The factorisation of 8x + 4y is:
A. 8(x+4y)
B. 4(2x+4y)
C. 8(x+y)
D. 4(2x+y)
Answer: D. 4(2x + y)
20. The factors of xyz are:
A. x
B. y
C. z
D. All of the above
Answer: D.
x, y and z are all the factors of xyz.
