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\left(2v^{2}-5\right)\left(4v^{2}+3\right)
Find one factor of the form kv^{m}+n, where kv^{m} divides the monomial with the highest power 8v^{4} and n divides the constant factor -15. One such factor is 2v^{2}-5. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: 2v^{2}-5,4v^{2}+3.