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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!