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c^{2}\left(c+9\right)+5\left(c+9\right)
Do the grouping c^{3}+9c^{2}+5c+45=\left(c^{3}+9c^{2}\right)+\left(5c+45\right), and factor out c^{2} in the first and 5 in the second group.
\left(c+9\right)\left(c^{2}+5\right)
Factor out common term c+9 by using distributive property. Polynomial c^{2}+5 is not factored since it does not have any rational roots.