Answer
$(2a-1)(5a-3)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
10a^2-11a+3
\end{array} has $ac=
10(3)=30
$ and $b=
-11
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-5,-6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
10a^2-5a-6a+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}
(10a^2-5a)-(6a-3)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5a(2a-1)-3(2a-1)
.\end{array}
Factoring the $GCF=
(2a-1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2a-1)(5a-3)
.\end{array}