[20pts] To evaluate a polynomial of degree n at v and v, one could simply call HornerEval twice, involving 2n multiplications and 2n additions. Describe and analyze an algorithm that uses HornerEval and solves this problem using only n+1 multiplications and n+1 additions (or subtractions). Hint: Split the coefficient array of the polynomial into even- and odd-indexed terms. A generalization of this process is the basis of the famous Fast Fourier Transform, which we will cover later in this course