Answer
$(2y-3)(3y+8) $
Work Step by Step
Factoring by grouping:
1. Multiply the leading coefficient, a, and the constant, c.
2. Find the factors of ac whose sum is b.
3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2.
4. Factor by grouping
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Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-132\qquad (6\times 24=2\times 3\times 3\times 8)$
2. $\quad$sum = $+7 \quad$... factors: $+16$ and $-9$
3. $\quad 6y^{2}+7y-24 =(6y^{2}-9y)+(16y-24)$
4. $\quad$... $=3y(2y-3)+(8)(2y-3) =(2y-3)(3y+8)$
Check by FOIL
$F:\quad 6y^{2}$
$O:\quad +16y$
$I:\quad -9y$
$L:\quad -24$
$(2y-3)(3y+8) $ = $6y^{2}+7y-24$
