Factorise : $n^{3} - 3 n - 2$ given that $n + 1$ is a factor. The factors are

{(n + 1)}^{2} (n - 2)

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(n + 1) {(n - 2)}^{2}

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{(n + 1)}^{2} (n + 2)

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none of these

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Solution

The correct option is C ${(n + 1)}^{2} (n - 2)$
the factors of $n^{3} - 3 n - 2$ are

$= n^{3} - 2 n^{2} + 2 n^{2} - 4 n + n - 2$

$= n^{2} (n - 2) + 2 n (n - 2) + 1 (n - 2)$

$= (n - 2) (n^{2} + 2 n + 1)$

$= (n - 2) (n + 1)^{2}$

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