Factorize the following
$x^{3} + 5 x^{2} - x - 5$

(x + 1) (x - 1) (x + 5)

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(x - 1) (x - 1) (x + 5)

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(x + 1) (x + 1) (x + 5)

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None of these

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Solution

The correct option is A $(x + 1) (x - 1) (x + 5)$
We factorize the given polynomial $x^{3} + 5 x^{2} - x - 5$ as shown below:
$x^{3} + 5 x^{2} - x - 5$

$= x^{2} (x + 5) - 1 (x + 5)$

$= (x^{2} - 1) (x + 5)$

$= (x + 1) (x - 1) (x + 5) (∵ a^{2} - b^{2} = (a + b) (a - b))$

Hence, $x^{3} + 5 x^{2} - x - 5 = (x + 1) (x - 1) (x + 5)$ .

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