Answer
$-(2x^{n}+1)(10x^n+3)$
Work Step by Step
Factoring the negative $GCF=
-1
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-20x^{2n}-16x^n-3
\\\\=
-1(20x^{2n}+16x^n+3)
\\\\=
-(20x^{2n}+16x^n+3)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-(20x^{2n}+16x^n+3)
\end{array} has $ac=
20(3)=60
$ and $b=
16
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
10,6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-(20x^{2n}+10x^n+6x^n+3)
.\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}
-[(20x^{2n}+10x^n)+(6x^n+3)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-[10x^n(2x^{n}+1)+3(2x^n+1)]
.\end{array}
Factoring the $GCF=
(2x^{n}+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-[(2x^{n}+1)(10x^n+3)]
\\\\=
-(2x^{n}+1)(10x^n+3)
.\end{array}
