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x^{5}\left(x-1\right)+3\left(x-1\right)
Do the grouping x^{6}-x^{5}+3x-3=\left(x^{6}-x^{5}\right)+\left(3x-3\right), and factor out x^{5} in the first and 3 in the second group.
\left(x-1\right)\left(x^{5}+3\right)
Factor out common term x-1 by using distributive property. Polynomial x^{5}+3 is not factored since it does not have any rational roots.