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\frac{6x^{5}-x^{4}+12x^{3}}{2}
Factor out \frac{1}{2}.
x^{3}\left(6x^{2}-x+12\right)
Consider 6x^{5}-x^{4}+12x^{3}. Factor out x^{3}.
\frac{x^{3}\left(6x^{2}-x+12\right)}{2}
Rewrite the complete factored expression. Polynomial 6x^{2}-x+12 is not factored since it does not have any rational roots.