a.) Show that the set $W$ of all polynomials in $P_2$ such that $p(1)=0$ is a subspace of $P_2$.
b.) Make a conjecture about the dimension of $W$.
c.) Confirm your conjecture by finding a basis for $W$.
I know how to show $W$ is a subspace of $P_2$, by showing closure under addition and multiplication by a scalar. However, I am clueless as to how to find a basis. I can't see how this is sufficient information to answer the question. All I can see is that if $p(1)=0$, then $a_01+a_1x+a_2x^2=0$ implies $$a_0+a_1+a_2=0$$