The first four Hermite polynomials are 1, 2t, minus2plus4t squared, and minus12tplus8t cubed. These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first four Hermite polynomials form a basis of set of prime numbers P 3. To show that the first four Hermite polynomials form a basis of set of prime numbers P 3, what theorem should be used? A. Let H be a subspace of a finite-dimensional vector space V. Any linearly independent set in H can be expanded, if necessary, to a basis for H. B. If a vector space V has a basis of n vectors, then every basis of V must consist of exactly n vectors. C. Let V be a p-dimensional vector space, pgreater than or equals1. Any linearly independent set of exactly p elements in V is automatically a basis for V.