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Remainder Theorem

Factorise the...

Question

Factorise the polynomial: $x^{2} - 1 + 2 a x + a^{2}$

(x - a - 1) (x + a - 1)

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(x + a + 1) (x + a - 1)

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(x + a + 1) (x - a + 1)

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(x - a + 1) (x + a - 1)

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Solution

The correct option is C $(x + a + 1) (x + a - 1)$
We have,
$x^{2} - 1 + 2 a x + a^{2}$

$\Rightarrow x^{2} + 2 a x + a^{2} - 1$

$\Rightarrow (x + a)^{2} - 1$ $∵ (x + y)^{2} = x^{2} + 2 x y + y^{2}$

$\Rightarrow (x + a)^{2} - 1^{2}$

$\Rightarrow (x + a + 1) (x + a - 1)$ $∵ x^{2} - y^{2} = (x + y) (x - y)$

Hence, this is the answer.

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