Factorise $9 x^{3} - 27 x^{2} - 100 x + 300$ given that 3x+10 is a factor

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Solution

$\frac{9 x^{3} - 27 x^{2} - 100 x + 300}{3 x + 10}$

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

$= (9 x^{3} - 27 x^{2}) + (- 100 x + 300)$

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

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

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

$= \frac{(x - 3) (3 x + 10) (3 x - 10)}{3 x + 10}$

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

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