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8r^{2}\left(8r+3\right)-3\left(8r+3\right)
Do the grouping 64r^{3}+24r^{2}-24r-9=\left(64r^{3}+24r^{2}\right)+\left(-24r-9\right), and factor out 8r^{2} in the first and -3 in the second group.
\left(8r+3\right)\left(8r^{2}-3\right)
Factor out common term 8r+3 by using distributive property. Polynomial 8r^{2}-3 is not factored since it does not have any rational roots.