What is the complete factor of $12 x^{3} + 24 x^{2} - 36 x$ ?

12 (x - 1) (x + 3)

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12 x (x + 1) (x + 3)

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(12 x - 1) (x + 3)^{2}

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12 x (x - 1) (x + 3)

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Solution

The correct option is D $12 x (x - 1) (x + 3)$
$12 x^{3} + 24 x^{2} - 36 x$
Take $12 x$ as common, we get
$= 12 x (x^{2} + 2 x - 3)$
$= 12 x (x^{2} - x + 3 x - 3)$ (replacing $2 x$ into $- x + 3 x$ to factorise easily)
$= 12 x (x (x - 1) + 3 (x - 1))$
So, $12 x (x - 1) (x + 3)$ is a complete factor.

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