Question: let v be the vector space of polynomials of degree...
Let V be the vector space of polynomials of degree 3 or less with the usual notion of addition and scalar multiplication. Let S be the subset of V where f ∈ S if, f(1) = 0 and f'(1) = 0.
(a) Prove that S is also a vector space.
(b) Find a basis for S.
(c) Verify that x3 + x2 − 5x + 3 ∈ S and find its coordinates with respect to the basis you found.