Question

Let V be the subspace of P3 spanned by the the following set
{1-x^2+x^3 , 2+x-x^2+x^3 , 1+2x+x^2-x^3}

(a) Show that f(x) = x + x^2 - x^3 ∈ V .
(b) Show that g(x) = 1 + x - x^2 +x^3 is not an element of V .
(c) Find a basis for V which contains f(x).
(d) Find a basis for P3 which contains g(x).