Resolve the following quadratic trinomial into factors:

$7 x - 6 x^{2} + 20$

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Solution

Given : $7 x - 6 x^{2} + 20$
$= - 6 x^{2} + 7 x + 20$
On splitting the middle term, we get
$- 6 x^{2} + 15 x - 8 x + 20$
$= - 3 x (2 x - 5) - 4 (2 x - 5)$
$= (- 3 x - 4) (2 x - 5)$
$= - (3 x + 4) (2 x - 5)$
$= (3 x + 4) (- 2 x + 5)$
$= (3 x + 4) (5 - 2 x)$

Hence, $7 x - 6 x^{2} + 20 = (3 x + 4) (5 - 2 x)$

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