Answer
$(4x-1)(2x-5)$
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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$8x^{2}-22x+5 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+40$
2. $\quad$sum = $-22 \quad$... factors: $-20$ and $-2$
3. $\quad$ $8x^{2}-22x+5 = (8x^{2}-2x)+( -20x-5)$
4. $\quad$... $=2x(4x-1) +(-5)(4x-1) = (4x-1)(2x-5)$
Check by FOIL
$F:\quad 8x^{2}$
$O:\quad -20x$
$I:\quad -2x$
$L:\quad +5$
$(4x-1)(2x-5)$ = $8x^{2}-22x+5$
