Answer
$ (3y+1)(5y-2) $
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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$15y^{2}-y-2 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-30\qquad $
2. $\quad$sum = $-1 \quad$... factors: $+5$ and $-6$
3. $\quad 15y^{2}-y-2 = (15y^{2}+5y)+(-6y-2)$
4. $\quad$... $= 5y(3y+1)+(-2)(3y+1)=(3y+1)(5y-2)$
Check by FOIL
$F:\quad 15y^{2}$
$O:\quad +5y$
$I:\quad -6y$
$L:\quad -2$
$ (3y+1)(5y-2) $ = $15y^{2}-y-2$
