This is closed under addition (the sum of two polynomials has degree equal to the max of their degrees), and is closed under multiplication (the degree of the product is the sum of the degrees). This ...This is closed under addition (the sum of two polynomials has degree equal to the max of their degrees), and is closed under multiplication (the degree of the product is the sum of the degrees). This set is closed under addition and multiplication, and is thus a subring. (The sum and product of two even integers is still even.) However, the even integers don't have the number 1, and so there is no unit in 2Z.
