space Solution Let\'s say we have a vector space P2 as the set of all 2nd degree polynomials of degree exactly 2. So let\'s take ax^2 + bx + c and -ax^2 +dx + e which are both in P2. Since P2 is a vector space, then it is closed under addition. If we added the two vectors above, we get a vector who\'s at most in the 1st degree. Does that help?.