P3 = {All functions of the form p(x) = ao + a1x + a2x² + a3x³}. Maybe you remember from calculus or another algebra class that x* is called a monomial. The polynomial vector spaces are the just a span of monomials. Specifically, Pa = span{1, x, x², ..., x“}. The dimension of this space is d+1 because of the number of monomials in the above space is d +1 and the set is linearly independent. There is also a set containing every polynomial. It can be written like this. d All functions p(x) where there is a whole number d so that p(x) = > `akx* k=0