(a) How many zeros can a polynomial with degree n != 0 have?
(b) definition of span
(c) definition of a basis
(d) definition of dimension
(e) that follows from rules how to calculate the derivative
(f) the (coordinates of the) images of the basis vectors form the columns of the associated matrix
That is a good exercise to get used to the concept of a vector space. You just have to follow definitions so there should not be any problems.