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2s^{2}\left(2s-1\right)+9\left(2s-1\right)
Do the grouping 4s^{3}-2s^{2}+18s-9=\left(4s^{3}-2s^{2}\right)+\left(18s-9\right), and factor out 2s^{2} in the first and 9 in the second group.
\left(2s-1\right)\left(2s^{2}+9\right)
Factor out common term 2s-1 by using distributive property. Polynomial 2s^{2}+9 is not factored since it does not have any rational roots.