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x^{2}\left(x-1\right)-11\left(x-1\right)
Do the grouping x^{3}-x^{2}-11x+11=\left(x^{3}-x^{2}\right)+\left(-11x+11\right), and factor out x^{2} in the first and -11 in the second group.
\left(x-1\right)\left(x^{2}-11\right)
Factor out common term x-1 by using distributive property. Polynomial x^{2}-11 is not factored since it does not have any rational roots.