Factorise
$x^{2} - x - 156$

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Solution

We have:

$x^{2} - x - 156$

We have to split (-1) into two numbers such that their sum is ( -1) and their product is (-156).

Clearly, $- 13 + 12 = - 1$ and $- 13 \times 12 = - 156$ .

$∴ x^{2} - x - 156 = x^{2} - 13 x + 12 x - 156 = x (x - 13) + 12 (x - 13) = (x - 13) (x + 12)$

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