Set of all polynomials that have zero order 3 in point 2
If I take polynomial $P_4(x)=(x-2)^3(x-3)$ and Polynomial $P_4(x)=(x-2)^3(x-1)$ and the sum of these two polynomials is $P_4(x)=2(x-2)^4$. This shows it does not belong in the set, so it is not a subspace, is this ok?