Factorize:
x² + 11x + 30

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Solution

We have:
$x^{2} + 11 x + 30$
We have to split 11 into two numbers such that their sum of is 11 and their product is 30.
Clearly, $5 + 6 = 11 and 5 \times 6 = 30$ .

$∴ x^{2} + 11 x + 30 = x^{2} + 5 x + 6 x + 30 = x (x + 5) + 6 (x + 5) = (x + 5) (x + 6)$

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