Answer
$2x^{2}(x+2)(4x^{3}-5x-4)$
Work Step by Step
$2 $ is a factor of all three terms
$x^{2}$ also, and so is
$(x+2).$
$GCF=2x^{2}(x+2)$
$ \begin{array}{ccc}
8x^{5}(x+2) & -10x^{3}(x+2) & -2x^{2}(x+2)=\\
=2x^{2}(x+2)\cdot 4x^{3} & +2x^{2}(x+2)\cdot(-5x) & +2x^{2}(x+2)\cdot(-4)
\end{array}$
= $2x^{2}(x+2)(4x^{3}-5x-4)$
