1. The problem statement, all variables and given/known data Simple enough: Is P2 a subspace of P3? 2. Relevant equations 3. The attempt at a solution I think it is. All P2's can be written in the form 0x^3 + ax^2 + bx + c. Then, it's easy to see that it's closed under scalar addition and multiplication. Our professor mentioned that R2 is NOT a subspace of R3, so that's throwing me off here. Anyone?