Factorize the following
$x^{3} + x^{2} - 4 x - 4$

(x + 1) (x + 2) (x - 2)

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(x - 1) (x + 2) (x - 2)

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(x + 1) (x - 2) (x - 2)

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None of these

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Solution

The correct option is A $(x + 1) (x + 2) (x - 2)$
We factorize the given polynomial $x^{3} + x^{2} - 4 x - 4$ as shown below:
$x^{3} + x^{2} - 4 x - 4 = x^{2} (x + 1) - 4 (x + 1) = (x + 1) (x^{2} - 4) = (x + 1) (x^{2} - 2^{2}) = (x + 1) (x + 2) (x - 2) (∵ a^{2} - b^{2} = (a + b) (a - b))$
Hence, $x^{3} + x^{2} - 4 x - 4 = (x + 1) (x + 2) (x - 2)$ .

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