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7x^{2}\left(9x-5\right)+9x-5
Do the grouping 63x^{3}-35x^{2}+9x-5=\left(63x^{3}-35x^{2}\right)+\left(9x-5\right), and factor out 7x^{2} in 63x^{3}-35x^{2}.
\left(9x-5\right)\left(7x^{2}+1\right)
Factor out common term 9x-5 by using distributive property. Polynomial 7x^{2}+1 is not factored since it does not have any rational roots.