I have to say initially I was going to say G(x) = 0 is definitely a polynomial!
Then I looked up the definition, just to be safe and the most widely used definition seems to be that a polynomial must have more than 1 term. I don't really understand why this definition is preferred(except for the fact that the root of the word poly is "many"). I have seen plenty of cases where constants are treated as polynomials of degree 0(the degree of a polynomial is the highest exponent the variable is raised to. Hence 0 = 0x^0 = 0*1 = 0. Or for any constant c, cx^0 = c*1 = c.
I'm sorry to provide such an ambivalent answer, but I hope I gave you at least one good reason to use for saying G(x) =0 is not a polynomial.
Id just point out that in mathematics definitions are very important so whatever class you are taking, figure out the definition of a polynomial and see if G(x) = 0 meets that definition.
Hope this was helpful,