Answer
$ (2y+9)(5y-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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$10y^{2}+43y-9 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-90\qquad $
2. $\quad$sum = $+43 \quad$... factors: $+45$ and $-2$
3. $\quad 10y^{2}+43y-9 = (10y^{2}+45y)+(-2y-9)$
4. $\quad$... $= 5y(2y+9)+(-1)(2y+9)=(2y+9)(5y-1)$
Check by FOIL
$F:\quad 10y^{2}$
$O:\quad -2y$
$I:\quad +45y$
$L:\quad -9$
$ (2y+9)(5y-1)$ = $10y^{2}+43y-9$
