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\left(y^{2}-6\right)\left(-y^{4}-6y^{2}-36\right)
Find one factor of the form ky^{m}+n, where ky^{m} divides the monomial with the highest power -y^{6} and n divides the constant factor 216. One such factor is y^{2}-6. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: -y^{4}-6y^{2}-36,y^{2}-6.