Question

Factorise the following:
(x²+x)² + 4(x² + x) - 12
Or
x + 3x² + 3x - 7
Your answer​

Answer 1

(1.)

GIVEN :–

• A polynomial (x²+x)² + 4(x² + x) - 12 = 0.

TO FIND :–

• Factors = ?

SOLUTION :–

$\\ \implies\bf ( {x}^{2} +x) ^{2} + 4( {x}^{2} + x) - 12 = 0$

• Put x² + x = t :–

$\\ \implies\bf (t)^{2} + 4(t) - 12 = 0$

• Splitting Middle term –

$\\ \implies\bf t^{2} + 6t - 2t- 12 = 0$

$\\ \implies\bf t(t + 6) - 2(t+6) = 0$

$\\ \implies\bf (t - 2)(t + 6) = 0$

• Now replace 't' –

$\\ \implies\bf ({x}^{2} +x- 2)({x}^{2} +x + 6) = 0$

• Again Splitting Middle term –

$\\ \implies\bf ({x}^{2} +2x - x- 2)({x}^{2} +x + 6) = 0$

$\\ \implies\bf \{x(x + 2) - 1(x + 2) \}({x}^{2} +x + 6) = 0$

$\\ \implies\bf (x - 1)(x + 2)({x}^{2} +x + 6) = 0$

$\\ \rule{220}{2}$

(2.)

GIVEN :–

• A polynomial x + 3x² + 3x - 7 = 0.

TO FIND :–

• Factors = ?

SOLUTION :–

$\\ \implies\bf x + 3 {x}^{2} + 3x - 7 = 0$

$\\ \implies\bf 3 {x}^{2} + 4x - 7 = 0$

• Splitting Middle term –

$\\ \implies\bf 3 {x}^{2} -3x + 7x - 7 = 0$

$\\ \implies\bf 3x(x - 1) + 7(x - 1) = 0$

$\\ \implies\bf (3x + 7)(x - 1)= 0$

$\\ \rule{220}{2}$