Question 867004
You are correct. 



According to this <a href="http://www.math.niu.edu/~beachy/courses/240/06spring/vectorspace.html">link</a>, it says 


<blockquote>     <font color="blue">"Closure: If u and v are any vectors in V, then the sum   u + v   belongs to V."</font>
</blockquote>

Both f(x) = 1 and g(x) = 1 belong to the vector space Q, but h(x) = f(x) + g(x) = 2 does NOT belong to the vector space Q (since h^2(x) = 4, h(x) = 2, h^2(x) doesn't equal h(x))


So because the closure rule doesn't hold for all elements in Q, this means Q is NOT a vector space.