Factorise:
$15 x^{2} + 2 x - 8$

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Solution

We have:

$15 x^{2} + 2 x - 8$

We have to split 2 into two numbers such that their sum is 2 and their product is (-120)

Clearly, $12 + - 10 = 2$ and $12 \times - 10 = - 120$ .

$∴ 15 x^{2} + 2 x - 8 = 15 x^{2} + 12 x - 10 x - 8 = 3 x (5 x + 4) - 2 (5 x + 4) = (5 x + 4) (3 x - 2)$

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