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