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\frac{4x^{3}+x^{2}}{2}
Factor out \frac{1}{2}.
x^{2}\left(4x+1\right)
Consider 4x^{3}+x^{2}. Factor out x^{2}.
\frac{x^{2}\left(4x+1\right)}{2}
Rewrite the complete factored expression.