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