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\left(5m^{2}-2\right)\left(m^{2}+3\right)
Find one factor of the form km^{n}+p, where km^{n} divides the monomial with the highest power 5m^{4} and p divides the constant factor -6. One such factor is 5m^{2}-2. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: 5m^{2}-2,m^{2}+3.