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