Answer
$(3y-4)(y+1) $
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.... none (other than 1).
1. $ac=-12$
2. sum = $-1$ ... factors: $-4$ and $+3$
3.
$3y^{2}-y-4=(3y^{2}+3y)+(-4y-4)$
4.
... $=3y(y+1)+(-4)(y+1)$
$=(3y-4)(y+1)$
Check by FOIL$\qquad (3y-4)(y+1) $=
$F:\quad 3y^{2}$
$O:\quad +3y$
$I:\quad -4y$
$L:\quad -4$
$(3y-4)(y+1) $= $3y^{2}-y-4$
