Factorize the following
$2 x^{2} + 15 - 27$

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Solution

$2 x^{2} + 15 x - 27$

Coefficient of $x^{2} = 2$ ; constant term $= - 27$

Their product $= 2 \times - 27 = - 54$

Coefficient of $x = 15$

$∴$ product $= - 54$ ; sum $= 15$

$2 x^{2} + 15 x - 27 = 2 x^{2} - 3 x + 18 x - 27$

$= x (2 x - 3) + 9 (2 x - 3)$

$= (2 x - 3) (x + 9)$

$∴ 2 x^{2} + 15 x - 27 = (2 x - 3) (x + 9)$

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