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