Factorize $9 x^{3} - 27 x^{2} - 100 x + 300$ .

(x - 3) (x + 5) (3 x + 0)

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(x - 3) (3 x + 10) (3 x - 10)

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(x + 3) (3 x - 3) (10 x + 3)

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(x - 5) (10 x + 3) (10 x - 3)

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Solution

The correct option is B $(x - 3) (3 x + 10) (3 x - 10)$
We have, $9 x^{3} - 27 x^{2} - 100 x + 300$
$= 9 x^{2} (x - 3) - 100 (x - 3)$

$= (x - 3) [9 x^{2} - 100]$

$= (x - 3) [(3 x)^{2} - 10^{2}]$

$= (x - 3) (3 x + 10) (3 x - 10)$

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