Factorise:
$x^{3} + 13 x^{2} + 32 x + 20$

(x + 1) (x + 2) (x + 10)

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(x - 1) (x + 2) (x - 10)

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(x - 1) (x - 2) (x + 10)

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(x + 1) (x - 2) (x - 10)

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Solution

The correct option is A $(x + 1) (x + 2) (x + 10)$
Let $f (x) = x^{3} + 13 x^{2} + 32 x + 20$

$f (- 1) = - 1 + 13 - 32 + 20 = 0$

Therefore, $x + 1$ is the factor of $f (x)$

On dividing $f (x)$ by $x + 1$ we get $x^{2} + 12 x + 20$

Therefore, $f (x) = (x + 1) (x^{2} + 12 x + 20)$

$⟹ f (x) = (x + 1) (x^{2} + 10 x + 2 x + 20)$

$⟹ f (x) = (x + 1) (x (x + 10) + 2 (x + 10))$

$⟹ f (x) = (x + 1) (x + 2) (x + 10)$

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