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