Find the factors of $3 x^{3} - x^{2} - 3 x + 1$

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Solution

$3 x^{3} - x^{2} - 3 x + 1 = 0$
$\Rightarrow x^{2} (3 x - 1) - 1 (3 x - 1) = 0$
$\Rightarrow (x^{2} - 1) (3 x - 1) = 0$
$\Rightarrow (x^{2} - 1) = 0, (3 x - 1) = 0$
$\Rightarrow (x - 1) = 0, (x + 1) = 0, (3 x - 1) = 0$
$∴ x = 1, - 1, \frac{1}{3}$

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