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\left(x-8A\right)\left(x+2A\right)
Consider x^{2}-6Ax-16A^{2} as a polynomial over variable x. Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor -16A^{2}. One such factor is x-8A. Factor the polynomial by dividing it by this factor.