Let b be the basis of p3 consisting of the hermite

Question

Question: Let B be the basis of P3 consisting of the Hermite polynomials in Exercise 21, and let p(t) = - 1 + 8t² + 8t³. Find the coordinate vector of p relative to B.

Exercise: The first four Hermite polynomials are 1, 2t, - 2 + 4t², and - 12t + 8t³ These polynomials arise naturally in the study of certain important differential equations in mathematical physics.2 Show that the first four Hermite polynomials form a basis of P₃.