Factorise the following polynomials
$2 x^{3} + 11 x^{2} - 7 x - 6$

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Solution

$2 x^{3} + 11 x^{2} - 7 x - 6 = 2 x^{3} - 2 x + 11 x^{2} - 5 x - 6 = 2 x (x^{2} - 1) + 11 x^{2} - 11 x + 6 x - 6 = 2 x (x - 1) (x + 1) + (11 x + 6) (x - 1)$
$= (x - 1) (2 x (x + 1) + 11 x + 6) = (x - 1) (2 x^{2} + 13 x + 6) = (x - 1) (2 x^{2} + 12 x + x + 6) = (x - 1) (2 x (x + 6) + (x + 6))$
$= (x - 1) (x + 6) (2 x + 1)$

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