Find vectors and a scalar that disprove that $A=\{p(x)\in V:p(0)-p(2)=2\}$ is a subspace of $V=R_3[x]$ So I am supposed to disprove that $A=\{p(x)\in V:p(0)-p(2)=2\}$ is a subspace of $V=R_3[x]$ by finding $v_1$, $v_2$, and $\alpha$ such that $v_1+\alpha v_2\notin A$. I am honestly kind of stumped here. So far, I have tried to play around with exponents and have found that $x^2-3x+2$ could work as $p$, however I don't think that I am even in the correct direction.
I don't think that I correctly understand the problem and can't seem to find any similar examples.

$0 \notin A$. So, just take any $v_1 \in A$ and $\alpha=-1$ and $v_2=v_1$.
