Answer
$(2x-1)(x+7)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression, $2x^2+13x-7,$ has $ac=
2(-7)=-14
$ and $b=
13
.$
The two numbers with a product of $ac$ and a sum of $b$ are $\left\{
-1,14
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
2x^2-x+14x-7
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{align*}
(2x^2-x)+(14x-7)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
x(2x-1)+7(2x-1)
.\end{align*}
Factoring the $GCF=
(2x-1)
$ of the entire expression above results to
\begin{align*}
(2x-1)(x+7)
.\end{align*}
