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

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Solution

Given: $x^{2} + x - 12$
$= x^{2} + 4 x - 3 x - 12$ , (split middle term so that resultant is same)
$= (x^{2} + 4 x) + (- 3 x - 12)$ , (group pair of terms)
$= x (x + 4) - 3 (x + 4)$ , (factor each binomials)
$= (x + 4) (x - 3)$ , (factor out common factor $(x + 4)$ )

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