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