Answer
$2x^2(16x^2+x+4)$
Work Step by Step
Factoring the $GCF=
2x^2
,$ the given expression, $
32x^4+2x^3+8x^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x^2
\left(
\dfrac{32x^4}{2x^2}+\dfrac{2x^3}{2x^2}+\dfrac{8x^2}{2x^2}
\right)
\\\\=
2x^2(16x^2+x+4)
.\end{array}