Factorize : 1) $x^{3} + 13 x^{2} + 32 x + 20$
2) $8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$

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Solution

$1) . x^{3} + 13 x^{2} + 32 x + 20$
$- 1$ is a root
$- 1 + 13 - 32 + 20 \to 0$
hence,
( diagram )
$\Rightarrow (x + 1) (x^{2} + 12 + 1)$

$2) . 8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$
$= {(2 a)}^{3} - b^{3} - 6 a b (2 a - b)$
$= {(2 a)}^{3} - b^{3} - 3 x (2 a) \times b (2 a - b)$
$= {(2 a - b)}^{3}$
Hence, solved.

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