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

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Solution

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

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

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