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