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4\left(8x^{3}+x\right)
Factor out 4.
x\left(8x^{2}+1\right)
Consider 8x^{3}+x. Factor out x.
4x\left(8x^{2}+1\right)
Rewrite the complete factored expression. Polynomial 8x^{2}+1 is not factored since it does not have any rational roots.