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\frac{5x^{3}+3x^{4}}{2}
Factor out \frac{1}{2}.
x^{3}\left(5+3x\right)
Consider 5x^{3}+3x^{4}. Factor out x^{3}.
\frac{x^{3}\left(3x+5\right)}{2}
Rewrite the complete factored expression.
\frac{5x^{3}+3x^{4}}{2}
Since \frac{5x^{3}}{2} and \frac{3x^{4}}{2} have the same denominator, add them by adding their numerators.