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3p^{2}\left(8p+5\right)-7\left(8p+5\right)
Do the grouping 24p^{3}+15p^{2}-56p-35=\left(24p^{3}+15p^{2}\right)+\left(-56p-35\right), and factor out 3p^{2} in the first and -7 in the second group.
\left(8p+5\right)\left(3p^{2}-7\right)
Factor out common term 8p+5 by using distributive property. Polynomial 3p^{2}-7 is not factored since it does not have any rational roots.