Factorise the following: $x^{2} - 4 x - 12$

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Solution

Given: $x^{2} - 4 x - 12$
$= x^{2} - 6 x + 2 x - 12$ (split the middle term)
$= (x^{2} - 6 x) + (2 x - 12)$ (group pair of terms)
$= x (x - 6) + 2 (x - 6)$ (factor each binomials)
$= (x - 6) (x + 2)$ (factor out common factor $(x - 6)$ )

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