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5x^{2}\left(x-9\right)-4\left(x-9\right)
Do the grouping 5x^{3}-45x^{2}-4x+36=\left(5x^{3}-45x^{2}\right)+\left(-4x+36\right), and factor out 5x^{2} in the first and -4 in the second group.
\left(x-9\right)\left(5x^{2}-4\right)
Factor out common term x-9 by using distributive property. Polynomial 5x^{2}-4 is not factored since it does not have any rational roots.