Prove or give counterexample [closed]

For each natural number n, let X be the set of polynomials of degree equal to n. Prove or give a counterexample: the set X is a vector space.

My teacher says it is NOT a vector space. I just need a little help proving it.

• If it is degree equal to $n$ (and not smaller or equal), then have a look at the axioms that need to be satisfied for something to be a vector space. Specifically, is there an identity element of addition (see en.wikipedia.org/wiki/Vector_space)? – Shinja Apr 24 '17 at 1:04

Let $p(x)$ be a polynomial belonging to X
In order for X to be a vector space, $-p(x)$ belongs to X
$p(x)+(-p(x))=0\in X$