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

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Solution

Let $p (x) = 2 x^{3} - 3 x^{2} - 3 x + 2$ $
$p (- 1) = 0$
Therefore, $(x + 1)$ is one of the factor.
The other factor is $2 x^{2} - 5 x + 2$
$\Rightarrow 2 x^{2} - x - 4 x + 2$
$\Rightarrow x (2 x - 1) - 2 (2 x - 1)$
$\Rightarrow (2 x - 1) (x - 2)$
$\Rightarrow 2 x^{3} - 3 x^{2} - 3 x + 2 = (x + 1) (2 x - 1) (x - 2)$

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