Answer
$(a-1)(25a+2)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
25a^2-23a-2
\end{array} has $ac=
25(-2)=-50
$ and $b=
-23
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-25,2
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
25a^2-25a+2a-2
.\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}
(25a^2-25a)+(2a-2)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
25a(a-1)+2(a-1)
.\end{array}
Factoring the $GCF=
(a-1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(a-1)(25a+2)
.\end{array}