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