Answer
$ (x+8)(3x-2) $
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
---
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=-48$
2. $\quad$sum = $+22 \quad$... factors: $+24$ and $-2$
3. $\quad 3x^{2}+22x-16 =(3x^{2}+24x)+( -2x-16)$
4. $\quad$... $=3x(x+8) +(-2)(x+8) =(x+8)(3x-2)$
Check by FOIL
$F:\quad 3x^{2}$
$O:\quad -2x$
$I:\quad +24x$
$L:\quad -16$
$ (x+8)(3x-2) $ = $3x^{2}+22x-16$
