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\frac{3x^{4}-16x}{4}
Factor out \frac{1}{4}.
x\left(3x^{3}-16\right)
Consider 3x^{4}-16x. Factor out x.
\frac{x\left(3x^{3}-16\right)}{4}
Rewrite the complete factored expression. Polynomial 3x^{3}-16 is not factored since it does not have any rational roots.