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2x^{2}\left(x-1\right)-3\left(x-1\right)
Do the grouping 2x^{3}-2x^{2}-3x+3=\left(2x^{3}-2x^{2}\right)+\left(-3x+3\right), and factor out 2x^{2} in the first and -3 in the second group.
\left(x-1\right)\left(2x^{2}-3\right)
Factor out common term x-1 by using distributive property. Polynomial 2x^{2}-3 is not factored since it does not have any rational roots.