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3m^{2}+\left(-5n+1\right)m+2n^{2}-n
Consider 3m^{2}-5mn+2n^{2}+m-n as a polynomial over variable m.
\left(m-n\right)\left(3m-2n+1\right)
Find one factor of the form km^{p}+q, where km^{p} divides the monomial with the highest power 3m^{2} and q divides the constant factor 2n^{2}-n. One such factor is m-n. Factor the polynomial by dividing it by this factor.