If you studied MATH111 then you will recall that a highest common factor of two polynomials , is a polynomial of highest degree which divides both and ; the polynomials are coprime if the only common factors are the constants. Assume has at least one linear factor. Since is distinct from and is not a root of any of , we deduce that and are coprime. Now we apply Theorem 7.2.7 in MATH111 to see that
for some real polynomials . Multiplying by , we obtain