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