Factorize:

(i) $x^{3} + 3 x^{2} + 3 x - 7$

(ii) $x^{3} - 3 x^{2} + 3 x + 7$ [4 MARKS]

Open in App

Solution

Application: 2 Marks each

$(i) x^{3} + 3 x^{2} + 3 x - 7 = (x^{3} + 3 x^{2} + 3 x + 1) - 8$ [Adding and subtracting 1]

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

$= {(x + 1) - 2} {(x + 1)^{2} + 2 (x + 1) + 2^{2}}$

$= (x + 1 - 2) (x^{2} + 2 x + 1 + 2 x + 2 + 4)$

$= (x - 1) (x^{2} + 4 x + 7)$

$(i i) x^{3} - 3 x^{2} + 3 x + 7 = (x^{3} - 3 x^{2} + 3 x - 1) + 8$ [Adding and subtracting 1]

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

$= (x - 1) + 2 {(x - 1)^{2} - (x - 1) \times 2 + 2^{2}}$

$= (x - 1 + 2) {(x - 1)^{2} - 2 (x - 1) + 4}$

$= (x + 1) (x^{2} - 2 x + 1 - 2 x + 2 + 4)$

$= (x + 1) (x^{2} - 4 x + 7)$

Suggest Corrections

Similar questions

x^{3} - 3 x^{2} + 3 x + 7

x^{3} + 3 x^{2} + 3 x + 7 = 0

Factories

1. x³-3x²+3x+7

Factories:

1. a⁹-b⁹

2. x³-3x²+3x+7

Join BYJU'S Learning Program