Let R be field of real numbers and R[x] the ring of polynomials in x with coefficients in R. Which of the following subsets of R[x] is a subring of R?

I) All polynomials whose coefficient of x is zero.

II) All polynomials whose degree is even integer, together with zero polynomial.

III) All polynomials whose coefficient are rational numbers.

THE ANSWER SAYS ONLY I AND III ARE CORRECT.

I DON'T GET WHY II IS NOT CORRECT.

--ITS COMPLETE IN ADDITION

--ITS ASSOCIATIVE

--IT HAS IDENTITY ELEMENT ZERO

--FOR EVERY POLYNOMIAL THERE IS AN ADDITIVE INVERSE WHICH WILL ALSO HAVE EVEN DEGREE

--ALSO ADDITION IS ABLIAN

--ITS COMPLETE IN MULTIPLICATION

--ITS ASSOCIATIVEI IN MULTIPLICATION