Factorise the following: $x^{2} + 7 x + 12$

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Solution

Given : $x^{2} + 7 x + 12$
$= x^{2} + 4 x + 3 x + 12$ [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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