Answer
$(2a+1)(a^2-7)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
2a^3+a^2-14a-7
,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(2a^3+a^2)-(14a+7)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
a^2(2a+1)-7(2a+1)
.\end{array}
Factoring the $GCF=
(2a+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2a+1)(a^2-7)
.\end{array}