Factorise:
$10 x^{2} - 9 x - 7$

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Solution

We have:
$10 x^{2} - 9 x - 7$

We have to split $- 9$ into two numbers such that their sum is $- 9$ and their product is $10 \times (- 7) = - 70$ ,

Clearly, $- 14 + 5 = - 9$ and $- 14 \times 5 = - 70$ .

$10 x^{2} - 9 x - 7 = 10 x^{2} + 5 x - 14 x - 7 = 5 x (2 x + 1) - 7 (2 x + 1) = (2 x + 1) (5 x - 7)$
$∴ 10 x^{2} - 9 x - 7 = (2 x + 1) (5 x - 7)$

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