1. The problem statement, all variables and given/known data If P is the set of all 4-degree polynomials, and W is the subset of all 4-degree polynomials such that p(-2) = p(2), find a set S such that W = span(S). 2. Relevant equations 3. The attempt at a solution My guess is that one set that works is x^4, x^2, and 1. My reasoning is that if x^3 is included, then you could take the coefficients of everything to be zero, and (-2)^3 =/= 2^3. Can't include x for similar reasons. Really not sure, I feel like it is possible to construct a polynomial where p(-2) = p(2) but does include an x^3 or an x.