I'm really confused about a question I came across in my textbook. It basically says this: Consider the set of polynomial functions of degree 2. Prove that this set is not closed under addition or scalar multiplication (and therefore not a vectorspace). I'm confused because I think it is closed under addition and scalar mult. example: f(x) = ax^2 + bx + c g(x) = dx^2 + ex + f (f+g)(x) = (a+d)x^2 + (b+e)x + (c+f) (sf)(x) = (sa)x^2 + (sb)x + sc both results should be in the set of polynomial functions of degree 2. Why would the question say it is not closed under addition and scalar mult. ?? Am I missing something very basic here, or could it be a trick question or something? Thanks!