Factorise the following: $x^{2} - 3 x - 18$ ;

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Solution

Given: $x^{2} - 3 x - 18$
$= x^{2} - 6 x + 3 x - 18$ (split the middle term)
$= (x^{2} - 6 x) + (3 x - 18)$ (group the pair of terms)
$= x (x - 6) + 3 (x - 6)$ (factor each binomials)
$= (x - 6) (x + 3)$ (factor out common factor $(x - 6)$ )

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