S does not span P2 (I'm guessing P2 means polynomials with order 2).  For polynomials, ax^2 + bx + c, S will yield only those with b = 0.

If P2 means the set of all polynomials of degree 2 or less, the given S does not span it, because there is no way to write non-constant LINEAR functions of x using multiples of elements of S.