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2\left(x^{3}+8x^{2}+4x+32\right)
Factor out 2.
x^{2}\left(x+8\right)+4\left(x+8\right)
Consider x^{3}+8x^{2}+4x+32. Do the grouping x^{3}+8x^{2}+4x+32=\left(x^{3}+8x^{2}\right)+\left(4x+32\right), and factor out x^{2} in the first and 4 in the second group.
\left(x+8\right)\left(x^{2}+4\right)
Factor out common term x+8 by using distributive property.
2\left(x+8\right)\left(x^{2}+4\right)
Rewrite the complete factored expression. Polynomial x^{2}+4 is not factored since it does not have any rational roots.