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x\left(x^{3}+3\right)+x^{3}+3
Do the grouping x^{4}+3x+x^{3}+3=\left(x^{4}+3x\right)+\left(x^{3}+3\right), and factor out x in x^{4}+3x.
\left(x^{3}+3\right)\left(x+1\right)
Factor out common term x^{3}+3 by using distributive property. Polynomial x^{3}+3 is not factored since it does not have any rational roots.