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x^{2}\left(2x+3\right)+2x+3
Do the grouping 2x^{3}+3+2x+3x^{2}=\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.