Answer
$(5x-11)(7x+4)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
35x^2-57x-44
\end{array} has $ac=
35(-44)=1540
$ and $b=
-57
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-77,20
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
35x^2-77x+20x-44
.\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}
(35x^2-77x)+(20x-44)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
7x(5x-11)+4(5x-11)
.\end{array}
Factoring the $GCF=
(5x-11)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5x-11)(7x+4)
.\end{array}