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

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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 $= - 15$

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

$= 2 x^{2} - 6 x - 9 x + 27$

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

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

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

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