Factorise :
(i) $x^{3} - 2 x^{2} - x + 2$

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Solution

$x^{3} - 2 x^{2} - x + 2$
$= x^{3} - x - 2 x^{2} + 2$
Grouping the $1^{s t}, 3^{r d}$ terms together and the $2^{n d}, 4^{t h}$ terms together.
$= x (x^{2} - 1) - 2 (x^{2} - 1)$
$= (x^{2} - 1) (x - 2)$
$[Using the identity, (a^{2} - b^{2}) = (a - b) (a + b)]$
$= (x - 1) (x + 1) (x - 2)$

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