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