Its roots will be multiples of the three complex cube roots of unity, so it can’t be factored in the reals.
Maybe the “completely” is inappropriate here? In my defense, that’s what textbooks at this level usually say when they mean “factor as far as possible using real, integer coefficients”.
All I was looking for was 2(z+2)(z^2-2z+4).
Its roots will be multiples of the three complex cube roots of unity, so it can’t be factored in the reals.
Maybe the “completely” is inappropriate here? In my defense, that’s what textbooks at this level usually say when they mean “factor as far as possible using real, integer coefficients”.
All I was looking for was 2(z+2)(z^2-2z+4).