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5r^{2}\left(r+6\right)+4\left(r+6\right)
Do the grouping 5r^{3}+30r^{2}+4r+24=\left(5r^{3}+30r^{2}\right)+\left(4r+24\right), and factor out 5r^{2} in the first and 4 in the second group.
\left(r+6\right)\left(5r^{2}+4\right)
Factor out common term r+6 by using distributive property. Polynomial 5r^{2}+4 is not factored since it does not have any rational roots.