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x^{2}\left(x+1\right)-10\left(x+1\right)
Do the grouping x^{3}+x^{2}-10x-10=\left(x^{3}+x^{2}\right)+\left(-10x-10\right), and factor out x^{2} in the first and -10 in the second group.
\left(x+1\right)\left(x^{2}-10\right)
Factor out common term x+1 by using distributive property. Polynomial x^{2}-10 is not factored since it does not have any rational roots.