Answer
$(3m+2)(m+4)$
Work Step by Step
When factoring $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b,$
and, if we find them, we rewrite $bx$ and proceed to factor in groups.
Here, factors of $3\times 8=24$ that add to $14$ are $+2$ and $+12.$
$3m^{2}+14m+8=3m^{2}+2m+12m+8$
$=\left(3m^{2}+2m\right)+(12m+8)$
$=m(3m+2)+4(3m+2)$
$=(3m+2)(m+4)$
