Answer
$(2y+3)(7y-3) $
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. $\quad ac=-126\qquad (2\times 63=2\times 7\times 9=2\times 3\times 3\times 7)$
2. $\quad$sum = $+15 \quad$... factors: $+21$ and $-6$
3. $\quad 14y^{2}+15y-9=(7y^{2}+21y)+(-6y-9)$
4. $\quad$... $=7y(2y+3)+(-3)(2y+3) =(2y+3)(7y-3)$
Check by FOIL
$F:\quad 14y^{2}$
$O:\quad -6y$
$I:\quad +21y$
$L:\quad -9$
$(2y+3)(7y-3) $ = $14y^{2}+15y-9$
