Factorise : $x^{3} - 3 x^{2} - x + 3 = 0$

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Solution

$x^{3} - 3 x^{2} - x + 3 = 0$

$x^{2} (x - 3) - 1 (x - 3) - 0$

$(x - 3) (x^{2} - 1) = 0$

$(x - 3) = 0$ $(x^{2} - 1) = 0$

$(x^{2} - 1) = 0 \Rightarrow x = \pm 1$ and $(x - 3) = 0 \Rightarrow x = 3$

$∴ x = - 1, 1, 3$

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