Answer
$(4x-1)(5x+8)$
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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$20x^{2}+27x-8 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-160 \quad$...$ (160=5\times 32)$
2. $\quad$sum = $+27\quad$... factors: $+32$ and $-5$
3. $\quad$ $20x^{2}+27x-8 = (20x^{2}-5x)+(32x-8 )$
4. $\quad$... $= 5x(4x-1)+8(4x-1) =(4x-1)(5x+8)$
Check by FOIL
$F:\quad 20x^{2}$
$O:\quad +32x$
$I:\quad -5x$
$L:\quad -8$
$(4x-1)(5x+8)$ = $20x^{2}+27x-8$
