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