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3x^{2}\left(3x+5\right)-7\left(3x+5\right)
Do the grouping 9x^{3}+15x^{2}-21x-35=\left(9x^{3}+15x^{2}\right)+\left(-21x-35\right), and factor out 3x^{2} in the first and -7 in the second group.
\left(3x+5\right)\left(3x^{2}-7\right)
Factor out common term 3x+5 by using distributive property. Polynomial 3x^{2}-7 is not factored since it does not have any rational roots.