Answer
$(4x+5)(2x+3)$
Work Step by Step
Using factoring of trinomials in the form $ax^2+bx+c,$ the given expression, $
8x^2+22x+15
,$ has $ac$ equal to $
8(15)=120
$ and $b$ equal to $
22
.$
The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{
10,12
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
8x^2+10x+12x+15
.\end{array}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(8x^2+10x)+(12x+15)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2x(4x+5)+3(4x+5)
.\end{array}
Factoring the $GCF=
(4x+5)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(4x+5)(2x+3)
.\end{array}
