Resolve the following quadratic trinomial into factors:
$3 + 23 y - 8 y^{2}$

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Solution

Given: $3 + 23 y - 8 y^{2}$
$= - 8 y^{2} + 23 y + 3$
On splitting the middle term , we get
$= - 8 y^{2} + 24 y - y + 3$
$= - 8 y (y - 3) - 1 (y - 3)$
$= (- 8 y - 1) (y - 3)$
$= - (8 y + 1) (y - 3)$
$= (8 y + 1) (- y + 3)$
$= (8 y + 1) (3 - y)$

Hence, $3 + 23 y - 8 y^{2} = (8 y + 1) (3 - y)$

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