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x^{3}\left(x-6\right)+6\left(x-6\right)
Do the grouping x^{4}-6x^{3}+6x-36=\left(x^{4}-6x^{3}\right)+\left(6x-36\right), and factor out x^{3} in the first and 6 in the second group.
\left(x-6\right)\left(x^{3}+6\right)
Factor out common term x-6 by using distributive property. Polynomial x^{3}+6 is not factored since it does not have any rational roots.