Answer
$(4k+3)(5k+8)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $ax^2+bx+c,$ find two numbers whose product is $ac$ and whose sum is $b$. Use these $2$ numbers to decompose the middle term of the quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
In the given expression, $
20k^2+47k+24
,$ the value of $ac$ is $
20(24)=480
$ and the value of $b$ is $
47
.$ The $2$ numbers that have a product $ac$ and a sum of $b$ are $\{
15,32
\}.$ Using these $2$ numbers to decompose the middle term of the given expression results to
\begin{array}{l}\require{cancel}
20k^2+15k+32k+24
.\end{array}
Grouping the first and third terms and the second and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(20k^2+15k)+(32k+24)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5k(4k+3)+8(4k+3)
.\end{array}
Factoring the $GCF=
(4k+3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(4k+3)(5k+8)
.\end{array}