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3m^{2}+5nm+2n^{2}
Consider 3m^{2}+5mn+2n^{2} as a polynomial over variable m.
\left(3m+2n\right)\left(m+n\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}. One such factor is 3m+2n. Factor the polynomial by dividing it by this factor.