Answer
$ (x+6)(7x+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. $\quad ac=+42$
2. $\quad$sum = $+43 \quad$... factors: $+42$ and $+1$
3. $\quad 7x^{2}+43x+6=(7x^{2}+42x)+( x+6)$
4. $\quad$... $=7x(x+6) +(1)(x+6) =(x+6)(7x+1)$
Check by FOIL
$F:\quad 7x^{2}$
$O:\quad +x$
$I:\quad +42x$
$L:\quad +6$
$ (x+6)(7x+1) $ = $7x^{2}+43x+6$
