Factorize $x^{3} - 3 x^{2} - 9 x - 5$

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

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(x - 1)^{2} (x - 5)

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

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None of the above

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Solution

The correct option is A $(x + 1)^{2} (x - 5)$
The value of $x^{3} - 3 x^{2} - 9 x - 5$ is
$x^{3} - 5 x^{2} + 2 x^{2} - 10 x + x - 5$
$= x^{2} (x - 5) + 2 x (x - 5) + 1 (x - 5)$
$= (x - 5) (x^{2} + 2 x + 1)$
$= (x - 5) (x + 1)^{2}$ $x^{3} - 3 x^{2} - 9 x - 5$
$= x^{3} - 5 x^{2} + 2 x^{2} - 10 x + x - 5$
$= x^{2} (x - 5) + 2 x (x - 5) + 1 (x - 5)$
$= (x - 5) (x^{2} + 2 x + 1)$
$= (x - 5) (x + 1)^{2}$

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