Class 8 Factorisation
Chapter 14: Factorisation
Ex 14.1
1. Find the common factors of the given terms.
(i) 12x, 36
(ii) 2y, 22xy
(iii) 14 pq, 28p² q²
(iv) 2x, 3x² , 4
(v) 6 abc, 24ab², 12 a²b
(vi) 16 x³, – 4x², 32x
(viii) 3x² y³ , 10x³ y² ,6 x² y² z
2. Factorise the following expressions
(i) 7x – 42
(ii) 6p – 12q
(iii) 7a²+ 14a
(iv) – 16 z + 20 z³
(v) 20 l2 m + 30 a l m
(vi) 5 x²y – 15 xy²
(vii) 10 a² – 15 b² + 20 c²
(viii) – 4 a² + 4 ab – 4 ca
(ix) x² y z + x y² z + x y z²
(x) a x² y + b x y² + c x y z
(i) x² + x y + 8x + 8y
(ii) 15 xy – 6x + 5y – 2
(iii) ax + bx – ay – by
(iv) 15 pq + 15 + 9q + 25p
(v) z – 7 + 7 x y – x y z
Ex 14.2
1. Factorise the following expressions.
(i) a²+ 8a + 16
(ii) p² – 10 p + 25
(iii) 25m² + 30m + 9
(iv) 49y² + 84yz + 36z²
(v) 4x² – 8x + 4
(vi) 121b²– 88bc + 16c²
(vii) (l + m)² – 4lm (Hint: Expand ( l + m)2 first)
2. Factorise.
(i) 4p² – 9q²
(ii) 63a² – 112b²
(iii) 49x² – 36
(iv) 16x⁵ – 144x³
(v) (l + m)² – (l – m)²
(vi) 9x² y²– 16
(vii) (x²– 2xy + y² ) – z²
(viii) 25a² – 4b²+ 28bc – 49c²
3. Factorise the expressions.
(i) ax² + bx
(ii) 7p²+ 21q²
(iii) 2x³ + 2xy²+ 2xz²
(iv) am² + bm²+ bn²+ an²
(v) (lm + l) + m + 1
(vi) y (y + z) + 9 (y + z)
(vii) 5y² – 20y – 8z + 2yz
(viii) 10ab + 4a + 5b + 2
(ix) 6xy – 4y + 6 – 9x
4. Factorise.
5. Factorise the following expressions.
(i) p² + 6p + 8
(ii) q² – 10q + 21
(iii) p² + 6p – 16
Ex 14.3
1. Carry out the following divisions.
(i) 28x⁴ ÷ 56x
(ii) –36y³÷ 9y²
(iii) 66pq² r³ ÷ 11qr²
(iv) 34x³ y³z³÷ 51xy² z³
(v) 12a⁸ b⁸÷ (– 6a⁶ b⁴ )
2. Divide the given polynomial by the given monomial.
(i) (5x²– 6x) ÷ 3x
(ii) (3y8 – 4y6 + 5y4 ) ÷ y4
(iii) 8(x3 y2 z2 + x2 y3 z2 + x2 y2 z3 ) ÷ 4×2 y2 z2
(iv) (x3 + 2×2 + 3x) ÷ 2x
(v) (p3 q6 – p6 q3 ) ÷ p3 q3
3. Work out the following divisions.
(i) (10x – 25) ÷ 5
(ii) (10x – 25) ÷ (2x – 5)
(iii) 10y(6y + 21) ÷ 5(2y + 7)
(iv) 9×2 y2 (3z – 24) ÷ 27xy(z – 8)
(v) 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)
(i) 5(2x + 1) (3x + 5) ÷ (2x + 1)
(ii) 26xy(x + 5) (y – 4) ÷ 13x(y – 4)
(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)
(iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)
(v) x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
5. Factorise the expressions and divide them as directed.
(i) (y2 + 7y + 10) ÷ (y + 5)
(ii) (m2 – 14m – 32) ÷ (m + 2)
(iii) (5p2 – 25p + 20) ÷ (p – 1)
(iv) 4yz(z2 + 6z – 16) ÷ 2y(z + 8)
(v) 5pq(p2 – q2 ) ÷ 2p(p + q)
(vi) 12xy(9×2 – 16y2 ) ÷ 4xy(3x + 4y)
(vii) 39y3 (50y2 – 98) ÷ 26y2 (5y + 7)
Ex 14.4
Find and correct the errors in the following mathematical statements.
1. 4(x – 5) = 4x – 5
2. x(3x + 2) = 3x2 + 2
3. 2x + 3y = 5xy
4. x + 2x + 3x = 5x
5. 5y + 2y + y – 7y = 0
6. 3x + 2x = 5x2
7. (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7
8. (2x)2 + 5x = 4x + 5x = 9x
9. (3x + 2)2 = 3x2 + 6x + 4
10. Substituting x = – 3 in
(a) x2 + 5x + 4 gives (– 3)2 + 5 (– 3) + 4 = 9 + 2 + 4 = 15
(b) x2 – 5x + 4 gives (– 3)2 – 5 ( – 3) + 4 = 9 – 15 + 4 = – 2
(c) x2 + 5x gives (– 3)2 + 5 (–3) = – 9 – 15 = – 24
11. (y – 3)2 = y2 – 9
12. (z + 5)2 = z2 + 25
13. (2a + 3b) (a – b) = 2a2 – 3b2
14. (a + 4) (a + 2) = a2 + 8
15. (a – 4) (a – 2) = a2 – 8
Ex 14.4 Factorisation free pdf download
Useful Links:
