Which of the following subsets of R[x] are subrings of R[x]? Justify your answer

A) All polynomials with constant term 0R.
B) All polynomials of degree 2
C) All polynomials of degree k less than or equal to k, where k is a fixed positive integer.

A) If you need 1 in your subring, then the answer is no.

Otherwise the sum and product of polynomials (in R[x]) without constant terms will again be without constant terms. (Then, the answer would be yes.)

B) No, x^2 * x^2 = x^4 is not of degree 2.

C) No, x^k * x^k = x^(2k) is not of degree k.

I hope this helps!