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x^{2}\left(x-5\right)+6\left(x-5\right)
Do the grouping x^{3}-5x^{2}+6x-30=\left(x^{3}-5x^{2}\right)+\left(6x-30\right), and factor out x^{2} in the first and 6 in the second group.
\left(x-5\right)\left(x^{2}+6\right)
Factor out common term x-5 by using distributive property. Polynomial x^{2}+6 is not factored since it does not have any rational roots.