Prove that the set of all polynomials of degree less than or equal to three (i.e., the set of all polynomials of the form p0 + p1x+ p2x2 + p3x3, where p0,p1,p2,p3 R) is a vector space over R. What is an example of a basis of this vector space? What are the components of the polynomial 5 + 2x2 with respect to this basis? Is 1,x+ 2,2x2,3x3 5 a basis? Prove this.