Factorise by splitting middle term
$3 x^{2} + 7 x + 2$

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Solution

Let $p (x) = 3 x^{2} + 7 x + 2$
Here we have to split middle term of p(x)
i.e. $7$ into two parts such that their sum is $7$ and product is $2 \times 3 = 6.$
$6$ and $1$ are such numbers whose sum is $7$ and product is $6$
$∴ 3 x^{2} + 7 x + 2 = 3 x^{2} + 6 x + x + 2$
$= 3 x (x + 2) + 1 (x + 2)$
$= (x + 2) (3 x + 1)$

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