1. The problem statement, all variables and given/known data Prove or disprove: there exists a basis (p_0, p_1, p_2, p_3) of P_3 (F) such that one of the polynomials p_0, p_1, p_2, p_3 has degree 2. 2. Relevant equations none really 3. The attempt at a solution Is the following proof correct? ---- Let p_0, p_1, p_2, p_3 be elements of P_3(F) s.t. p_o (x) = 1, p_1 (x) = x, p_2 (x) = x^2 + x^3, p_3(x) = x^3. None of the polynomials are degree 2 although (p_0,p_1,p_2,p_3) is clearly spanning P_3 (F) with dimP_3(F) = 4 and forms a basis. Hence proved.