#### Answer

$(a-4)(2b^2+1)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
2ab^2-8b^2+a-4
,$ 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}
(2ab^2-8b^2)+(a-4)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2b^2(a-4)+(a-4)
.\end{array}
Factoring the $GCF=
(a-4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(a-4)(2b^2+1)
.\end{array}