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