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8x^{2}\left(9x-8\right)+9x-8
Do the grouping 72x^{3}-64x^{2}+9x-8=\left(72x^{3}-64x^{2}\right)+\left(9x-8\right), and factor out 8x^{2} in 72x^{3}-64x^{2}.
\left(9x-8\right)\left(8x^{2}+1\right)
Factor out common term 9x-8 by using distributive property. Polynomial 8x^{2}+1 is not factored since it does not have any rational roots.