Important questions for Class 8 Maths Chapter 14 factorization
These factorization extra questions will help CBSE students to be well-prepared for the Class 8 exam
1. Express the following as in the form of (a+b)(a-b)
(i) a2 – 64
(ii) 20a2 – 45b2
(iii) 32x2y2 – 8
(iv) x2 – 2xy + y2 – z2
(v) 49x2 – 1
2. For a = 3, simplify a2 + 5a + 4 and a2 – 5a
3. Find the common factors of the following:
(i) 6 xyz, 24 xy2 and 12 x2y
(ii) 3x2 y3, 10x3 y2 and 6x2 y2 z
4. Factorize the following expressions:
(i) 54x3y + 81x4y2
(ii) 14(3x – 5y)3 + 7(3x – 5y)2
(iii) 15xy + 15 + 9y + 25x
5. Solve for (4x2 – 100) ÷ 6(x + 5)
Factorise the following polynomials.
(a) 6p(p – 3) + 1 (p – 3)
(b) 14(3y – 5z)3 + 7(3y – 5z)2
Factorise the following:
(a) p2q – pr2 – pq + r2
(b) x2 + yz + xy + xz
Factorise:
(a) a2 + 14a + 48
(b) m2 – 10m – 56
Factorise the given expressions and divide that as indicated.
(a) 39n3(50n2 – 98 ) ÷ 26n2(5n – 7)
(b) 44(p4 – 5p3 – 24p2) ÷ 11p(p – 8)
1. Factorise : 27x3 – 21x2 + 15x4
2. Factorise : ax3y2 + bx2y3 + cx2y2z
3. Factorise : x – 9 + 9zy – xyz
4. Factorise:
(i) p2 – 8p + 16
ii) 121x2 + 44xy + 4y2
5. Factorise: 54x2 – 96y2
6. Divide 63(p4 + 5p3 – 24p2) by 9p(p + 8).
MULTIPLE CHOICE QUESTIONS
1. Which of the following is the common factor of 21 x2y and 35 xy2?
(i) 7
(ii) xy
(iii) 7 xy
(iv) none of these.
2. Which of the following arc the factors of 1 – x2?
(i) (x + l) (x – I)
(ii) (1 – x) (1 + x)
(iii) (1 – x) (1 – x)
(iv) (1 + x) (1 + x).
3. Which of the following is the common factor of:
5xy, 3pqr and 40 xyz?
(i) 5
(ii) 0
(iii) xy
(iv) 1
4. Which of the following is quotient obtained on dividing –18 xyz2 by –3 xz?
(i) 6 Yz
(ii) –6 yz
(iii) 6 xy2
(iv) 6 xy
5. Which of the following is quotient obtained on dividing (x2 – b) (x – a) by –(x – a)?
(i) (x2 – b)
(ii) 
(iii) –(x2 – b)
(iv) – (x + a)
6. Which of the following are the factors of a2 + ab + bc + ca
(i) ab – a – b + 1 = (1 – a)(1 – b)
(ii) ab – a – b + 1 = (a – 1)(b – 1)
(iii) ab – a – b + 1 = (1 – a)(b – 1)
(iv) ab – a – b + 1 = (a – 1)(1 – b)
7. (y – x) (y + x) is equal to which of the following:
(i) y2 – yx
(ii) yx – x2
(iii) y2 – x2
(iv) x2 – y2
8. Which of the following are the factors of a2 + ab +bc + ca
(i) (b + c) (c + a)
(ii) (a + b) (a + c)
(iii) a(a + b + c)
(iv) (a + b) (b + c).
9. Which of the following is the factorisation of x3 – x?
(i) x(x – x2)
(ii) x[(1+ x) (1 – x)]
(iii) x(x2 – x)
(iv) x[(x + 1) (x – 1)]
10. Which of the following is equal to x3 – 225x
(i) x(1 – 15x) (1 + 15x)
(ii) x(x – 15) (x + 15)
(iii) x(1 – 15x) (1 – 15x)
(iv) x(1 + 15x) (1 – 15x).
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