Question

2. Factorise each of the following expressions:
a) 7x2 + 43x + 36
b) 6x2 + 13x + 2
e) 262 + 17b + 35 f) 2.x2 - x - 3
i) 6x2 – 39x – 21 j) -9x2 – 27x – 20
m) 4x2 -- 17x + 4 n) 4x2 + 12xy +9y
q) 25p2 + 81q2 – 90pq r) 9m2 + 12mn + 4n2
u 12a+ + 7a - 10 V) y2 + y - 72
x) (b + 4)2 + 4(b + 4) - 21​

Answer 1

★Question:

2. Factorise each of the following expressions:

a) 7x2 + 43x + 36

b) 6x2 + 13x + 2

$\:$

e) 262 + 17b + 35 f) 2.x2 - x - 3

i) 6x2 – 39x – 21 j) -9x2 – 27x – 20

m) 4x2 -- 17x + 4 n) 4x2 + 12xy +9y

q) 25p2 + 81q2 – 90pq r) 9m2 + 12mn + 4n2

u 12a+ + 7a - 10 V) y2 + y - 72

x) (b + 4)2 + 4(b + 4) - 21

★Answer:

$a) \: \: 7x {}^{2} + 43x + 36 \\ = 7x {}^{2} + (36 + 7)x + 36 \\ = {7x}^{2} + 36x + 7x + 36 \\ = x(7x + 36) + 1(7x +36) \\ = (7x +36)(x + 1)$

$\\ \\ b) \: \: 6x {}^{2} + 13x + 2 \\ = 6x {}^{2} + (12 + 1) x+ 2 \\ = 6x {}^{2} + 12x + 1x + 2 \\ = 6x(x + 2) + 1(x + 2) \\ = (x + 2)(6x + 1)$

$f) \: \: 2 {x}^{2} - x - 3 \\ =2x {}^{2} - (3 - 2)x - 3 \\ = 2x {}^{2} - 3x + 2x - 3 \\ = x(2x - 3) + 1(2x - 3) \\ = (x + 1)(2x - 3)$

$m) \: \: 4x {}^{2} -17x + 4 \\ = 4 {x}^{2} - (16 + 1)x + 4 \\ = 4 {x}^{2} - 16x - x + 4 \\ = 4x(x - 4) - 1(x - 4) \\ = (x - 4) (4x - 1)$