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c^{3}\left(c+4\right)+7\left(c+4\right)
Do the grouping c^{4}+4c^{3}+7c+28=\left(c^{4}+4c^{3}\right)+\left(7c+28\right), and factor out c^{3} in the first and 7 in the second group.
\left(c+4\right)\left(c^{3}+7\right)
Factor out common term c+4 by using distributive property. Polynomial c^{3}+7 is not factored since it does not have any rational roots.