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3m-2n+x^{4}\left(3m-2n\right)
Do the grouping 3m-2n-2nx^{4}+3mx^{4}=\left(3m-2n\right)+\left(-2nx^{4}+3mx^{4}\right), and factor out x^{4} in -2nx^{4}+3mx^{4}.
\left(3m-2n\right)\left(1+x^{4}\right)
Factor out common term 3m-2n by using distributive property. Polynomial x^{4}+1 is not factored since it does not have any rational roots.