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

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Solution

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

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