Factorise the following: $2 x^{2} + 7 x + 6$

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Solution

Given: $2 x^{2} + 7 x + 6$
$= 2 x^{2} + 3 x + 4 x + 6$ , (split the middle term so that resultant is same)
$= (2 x^{2} + 3 x) + (4 x + 6)$ , (group pair of terms)
$= x (2 x + 3) + 2 (2 x + 3)$ , (factor each binomials)
$= (2 x + 3) (x + 2)$ , (factor out commmon factor $(2 x + 3)$ )

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