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\left(w^{2}+9\right)\left(w^{2}-7\right)
Find one factor of the form w^{k}+m, where w^{k} divides the monomial with the highest power w^{4} and m divides the constant factor -63. One such factor is w^{2}+9. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: w^{2}-7,w^{2}+9.