Factorise $x^{3} - 23 x^{2} + 142 x - 120$

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Solution

$x^{3} - 23 x^{2} + 142 x - 120$
= $x^{3} - x^{2} - 22 x^{2} + 22 x + 120 x - 120$
= $x^{2} (x - 1) - 22 x (x - 1) + 120 (x - 1)$
= $(x - 1) (x^{2} - 22 x + 120)$
= $(x - 1) [x^{2} - 10 x - 12 x + 120]$
= $(x - 1) [x (x - 10) - 12 (x - 10)]$
= $(x - 1) (x - 10) (x - 12)$

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x^{3} - 23 x^{2} + 142 x - 120

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(x - 1)

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