Factorise : $2 x^{3} + 5 x^{2} - 5 x - 2$

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Solution

$2 x^{3} + 5 x^{2} - 5 x - 2$
$= 2 x^{3} - 2 + 5 x^{2} - 5 x$
$= 2 (x^{3} - 1) + 5 x (x - 1)$
$= 2 (x - 1) (x^{2} + x + 1) + 5 x (x - 1)$
$= (x - 1) (2 x^{2} + 2 x + 2 + 5 x)$
$= (x - 1) (2 x^{2} + 7 x + 2)$

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