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\left(y^{2}-8\right)\left(y^{2}+5\right)
Find one factor of the form y^{k}+m, where y^{k} divides the monomial with the highest power y^{4} and m divides the constant factor -40. One such factor is y^{2}-8. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: y^{2}-8,y^{2}+5.