Answer
$2(5a-9)(a+1)$
Work Step by Step
Factoring the $GCF=
2
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
10a^2-8a-18
\\\\=
2(5a^2-4a-9)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
2(5a^2-4a-9)
\end{array} has $ac=
5(-9)=-45
$ and $b=
-4
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-9,5
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
2(5a^2-9a+5a-9)
.\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}
2[(5a^2-9a)+(5a-9)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2[a(5a-9)+(5a-9)]
.\end{array}
Factoring the $GCF=
(5a-9)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
2[(5a-9)(a+1)]
\\\\=
2(5a-9)(a+1)
.\end{array}
