Answer
$(y-1)(5y-3)$
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. $\quad ac=+15$
2. $\quad$sum = $-8 \quad$... factors: $-5$ and $-3$
3. $\quad 5y^{2}-8y+3=(5y^{2}-5y)+(-3y+3)$
4. $\quad$... $=5y(y-1)+(-3)(y-1) =(y-1)(5y-3)$
Check by FOIL
$F:\quad 5y^{2}$
$O:\quad -3y$
$I:\quad -5y$
$L:\quad +3$
$(y-1)(5y-3)$ = $5y^{2}-8y+3$
