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