Resolve the following quadratic trinomial into factors:
$3 x^{2} + 22 x + 35$

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Solution

Given: $3 x^{2} + 22 x + 35$
On splitting the middle term, we get
$3 x^{2} + 15 x + 7 x + 35$
$= 3 x (x + 5) + 7 (x + 5)$
$= (3 x + 7) (x + 5)$

Hence, $3 x^{2} + 22 x + 35 = (3 x + 7) (x + 5)$

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