How to solve this question?

Problem 1. For each n E N, let Pn be the vector space of all polynomials of degree at most n. In each of (a) - (d) below, find a basis B of the given vector space V that satisfies the given conditions. P(0) (a) V = P2, and [pls = p'(0) for all pe P2. P"(0) p(a) (b) V = Pn, and [p]s = for all p E Pn, where a is a fixed constant in R. Lp(m) (a) P(0) (c) V = P2, and [p]s = p(1) P(2) for all p EP2. p(al) (d) V = Pm, and [p]s = for all p 6 Pn, where a1, . .., an+1 are distinct real numbers. Lp(an+1)]