Answer
$-(3t^{5}+2)^2$
Work Step by Step
Factoring the negative $GCF=
-1
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-9t^{10}-12t^5-4
\\\\=
-1(9t^{10}+12t^5+4)
\\\\=
-(9t^{10}+12t^5+4)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-(9t^{10}+12t^5+4)
\end{array} has $ac=
9(4)=36
$ and $b=
12
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
6,6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-(9t^{10}+6t^5+6t^5+4)
.\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}
-[(9t^{10}+6t^5)+(6t^5+4)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-[3t^5(3t^{5}+2)+2(3t^5+2)]
.\end{array}
Factoring the $GCF=
(3t^{5}+2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-[(3t^{5}+2)(3t^5+2)]
\\\\=
-(3t^{5}+2)^2
.\end{array}
