#### Answer

$-2x^{3}(x-4)(5x-2)$

#### Work Step by Step

$-10x^{5}+44x^{4}-16x^{3}\qquad$...factor out the common term, $-2x^{3}$
$=-2x^{3}(5x^{2}-22x+8)$
... Searching for two factors of $ac=40$ whose sum is $b=-22,$
we find$\qquad-20$ and $-2.$
Rewrite the middle term and factor in pairs:
$=-2x^{3}(5x^{2}-20x-2x+8)=$
$=-2x^{3}[5x(x-4)-2(x-4)]$
=$-2x^{3}(x-4)(5x-2)$