If , then either

Case 1

is of degree and is of degree ,

or

Case 2

is of degree and is of degree

I'll do case 1

But the polynomials have integer coefficients, so and

(I'm going to choose for both to simplify things here)

Expanding

Comparing coefficients

, so

, so

, so

, so

Contradiction has occurred, so Case 1 is impossible

Case 2 is proven similarly