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\left(2m^{2}-5\right)\left(2m^{2}+5\right)
Rewrite 4m^{4}-25 as \left(2m^{2}\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right). The following polynomials are not factored since they do not have any rational roots: 2m^{2}-5,2m^{2}+5.