Answer
$ (x+4)(8x+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
---
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+32$
2. $\quad$sum = $+33 \quad$... factors: $+32$ and $+1$
3. $\quad 8x^{2}+33x+4=(8x^{2}+32x)+( x+4)$
4. $\quad$... $=8x(x+4) +(1)(x+4) =(x+4)(8x+1)$
Check by FOIL
$F:\quad 8x^{2}$
$O:\quad +x$
$I:\quad +32x$
$L:\quad +4$
$ (x+4)(8x+1) $ = $8x^{2}+33x+4$
