Answer
$-(5x+2)(7x+4)$
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^2-34x-8
\end{array} has $ac=
-35(-8)=280
$ and $b=
-14,-20
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
15,16
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-35x^2-14x-20x-8
.\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^2-14x)-(20x+8)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-7x(5x+2)-4(5x+2)
.\end{array}
Factoring the $GCF=
(5x+2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5x+2)(-7x-4)
\\\\=
-(5x+2)(7x+4)
.\end{array}