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5x^{2}\left(x+2\right)-16\left(x+2\right)
Do the grouping 5x^{3}+10x^{2}-16x-32=\left(5x^{3}+10x^{2}\right)+\left(-16x-32\right), and factor out 5x^{2} in the first and -16 in the second group.
\left(x+2\right)\left(5x^{2}-16\right)
Factor out common term x+2 by using distributive property. Polynomial 5x^{2}-16 is not factored since it does not have any rational roots.