Answer
$ (x+4)(3x+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. $ac=12$
2. sum = $13$... factors: $1$ and $12$
3.
$3x^{2}+13x+4=(3x^{2}+ x)+(12x+4)$
4.
... $=x(3x+1)+4(3x+1)$
$=(x+4)(3x+1)$
Check by FOIL$\qquad (x+4)(3x+1) $=
$F:\quad 3x^{2}$
$O:\quad +x$
$I:\quad +12x$
$L:\quad +4$
$ (x+4)(3x+1) $= $3x^{2}+13x+4$
