Answer
$(y+1)(9y-4)$
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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$9y^{2}+5y-4 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-36$
2. $\quad$sum = $+5\quad$... factors: $+9$ and $-4$
3. $\quad$ $9y^{2}+5y-4 = ( 9y^{2}+9y)+(-4y-4)$
4. $\quad$... $= 9y(y+1)+(-4)(y+1) = (y+1)(9y-4)$
Check by FOIL
$F:\quad 9y^{2}$
$O:\quad -4y$
$I:\quad +9y$
$L:\quad -4$
$(y+1)(9y-4)$ = $9y^{2}+5y-4$
