Answer
$(4k+7)(2k+5)$
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, $
8k^2+34k+35
,$ the value of $ac$ is $
8(35)=280
$ and the value of $b$ is $
34
.$ The $2$ numbers that have a product $ac$ and a sum of $b$ are $\{
14,20
\}.$ Using these $2$ numbers to decompose the middle term of the given expression results to
\begin{array}{l}\require{cancel}
8k^2+14k+20k+35
.\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}
(8k^2+14k)+(20k+35)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2k(4k+7)+5(4k+7)
.\end{array}
Factoring the $GCF=
(4k+7)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(4k+7)(2k+5)
.\end{array}
