Factorize the following
$x^{2} + 2 x - 15$

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Solution

$x^{2} + 2 x - 15$

To factorize we have to find $p$ and $q$ , such that $p q = - 15$ and $p + q = 2$

$x^{2} + 2 x - 15$

$= x^{2} - 3 x + 5 x - 15$

$= x (x - 3) + 5 (x - 3)$

$= (x - 3) (x + 5)$

$∴ x^{2} + 2 x - 15 = (x - 3) (x + 5)$

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