Answer
$ (x+3)(2x+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.... none (other than 1).
1. $ac=6$
2. sum = $7$... factors: $1$ and $6$
3.
$2x^{2}+7x+3=(2x^{2}+ x)+(6x+3)$
4.
... $=x(2x+1)+3(2x+1)$
$=(x+3)(2x+1)$
Check by FOIL$\qquad (x+3)(2x+1) $=
$F:\quad 2x^{2}$
$O:\quad +x$
$I:\quad +6x$
$L:\quad +3$
$ (x+3)(2x+1) $= $2x^{2}+7x+3$
