Answer
$(x+3)(4x+5)$
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=4, b=17, $ and $c=15$.
To factor the trinomial using the AC-method, perform the following steps:
(1) FInd the value of $a\cdot c$.
$$ac=4(15)=60$$
(2) Look for factors $d$ and $e$ of $ac$ such that $d+e=b$.
Note that $12(5)=60$ and $12+5=17$.
Thus, $d=12$ and $e=5$.
(3) Rewrite the trinomial in the form $ax^2+dx+ex+c$ to obtain:
$$4x^2+17x+15=4x^2+12x+5x+15$$
(4) Factor $ax^2+dx^ex=c$ by grouping:
\begin{align*}
4x^2+12x=5x=15&=(4x^2+12x)+(5x+15)\\
&=4x(x+3)+5(x+3)\\
&=(x+3)(4x+5)\\
\end{align*}
