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w^{2}\left(w-6\right)+3\left(w-6\right)
Do the grouping w^{3}-6w^{2}+3w-18=\left(w^{3}-6w^{2}\right)+\left(3w-18\right), and factor out w^{2} in the first and 3 in the second group.
\left(w-6\right)\left(w^{2}+3\right)
Factor out common term w-6 by using distributive property. Polynomial w^{2}+3 is not factored since it does not have any rational roots.