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

(x + 1) (x - 1) (x - 3)

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(x - 1) (x - 1) (x - 3)

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(x + 1) (x + 1) (x - 3)

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None of these

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Solution

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

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

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