Suppose that p_0,p_1,p_2.......,p_m are polynomials in Pm(F) such that p_j(2)=0 for each j. Prove that (p_0,........,p_m) is not linearly independent in Pm(F). So far I have, suppose that there is a polynomial in the list that is of degree 0, then that polynomial must be 0, hence the list is linearly dependent. If there is no polynomial of degree zero, there are at least two polynomials in the list that have the same degree. This where I get stuck, am I going in the right direction?