Your statement is very vague. These are polynomials over what? An integral domain? An arbitrary ring? A field? The real numbers? It's very important that you specify.

Do you know the axioms for a field? If so, and you know what your polynomials are, you just have to verify each of the axioms : show that it is an abelian group under addition, that the nonzero elements form an abelian group under multiplication, that multiplication is distributive over addition, etc.