Jose S. | Friendly Mathematics, Philosophy, and Computer Science tutorFriendly Mathematics, Philosophy, and Co...
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,
Darlene N. | Experienced Math Teacher and Doctoral Candidate in Math EducationExperienced Math Teacher and Doctoral Ca...
5.05.0(3 lesson ratings)(3)
Anything with "poly-" as a prefix always means more than one, whether in math or any other use (polygon = more than one side; polygamy = more than one wife; etc). The root word "nomial" means name or term. So just looking at the word, polynomial means more than one term.
Any function that is constant or consists of only one term is called a monomial, since "mono-" means one. I've always liked when mathematicians stick with words that make sense in regular language. :)