Answer
$2x(5x-2)(25x^{2}+10x+4)$
Work Step by Step
Step 1: $250x^{4}-16x$
Step 2: The two terms have a common factor of $2x$, which we factor out:
$250x^{4}-16x=2x(125x^{3}-8)$.
Step 3: $2x((5x)^{3}-(2)^{3})$
Step 4: $2x(5x-2)((5x)^{2}+(5x)(2)+2^{2})$
Step 5: $2x(5x-2)(25x^{2}+10x+4)$
Step 6: No further factorization possible.