Factorise: $4 x^{3} + 4 x^{2} - x - 1$

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Solution

$4 x^{3} + 4 x^{2} - x - 1$
$= 4 x^{2} (x + 1) - 1 (x + 1)$
$= (x + 1) (4 x^{2} - 1)$
$= (x + 1) (2 x - 1) (2 x + 1)$

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