Resolve the following quadratic trinomial into factors:
$28 - 31 x - 5 x^{2}$

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Solution

Given: $28 - 31 x - 5 x^{2}$
$= - 5 x^{2} - 31 x + 28$
On splitting the middle term, we get
$= - 5 x^{2} - 35 x + 4 x + 28$
$= - 5 x (x + 7) + 4 (x + 7)$
$= (x + 7) (- 5 x + 4)$
$= (x + 7) (4 - 5 x)$

Hence, $28 - 31 x - 5 x^{2} = (x + 7) (4 - 5 x)$

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