Recall the vector space P(3) consisting of all polynomials in the variable x of degree at most 3. Consider the following collections, X, Y, Z, of elements of P(3).
X := {0, x, x² + 3, x³},
Y :={1, x + 1, (x − 1) · (x + 1), 3 ⋅ x³},
Z := {x³ + x² + x + 1, x² + 1, x + 1, x, 1, 0}.

In each case decide if the statement is true or false. (A) span(X) = P(3). (______)
(B) span(Z) = P(3). (______)
(C) Y is a basis for P(3). (______)
(D) Z is a basis for P(3). (______)