Answer
$(x+2)(3x+4)$
Work Step by Step
Recall:
Some trinomials of the form $ax^2+bx+c$ can be factored using the AC-method.
The given trinomial has $a=3, b=10, $ and $c=8$.
To factor the trinomial using the AC-method, perform the following steps:
(1) FInd the value of $a\cdot c$.
$$ac=3(8)=24$$
(2) Look for factors $d$ and $e$ of $ac$ such that $d+e=b$.
Note that $6(4)=24$ and $6+4=10$.
Thus, $d=6$ and $e=4$.
(3) Rewrite the trinomial in the form $ax^2+dx+ex+c$ to obtain:
$$3x^2+10x+8=3x^2+6x+4x+8$$
(4) Factor $ax^2+dx+ex+c$ by grouping:
\begin{align*}
3x^2+6x+4x+8&=(3x^2+6x)+(4x+8)\\
&=3x(x+2)+4(x+2)\\
&=(x+2)(3x+4)\\
\end{align*}
