Let o, 1m ER be pairwise distinct and let f: R R be a function. We write plak, +1,...,] for the polynomial of degree 1-k that interpolates f at the points #k, k+1,..., , where k1. Show that (p,m]-p[ro, 1,,m-1]) plo, 1, Em] p[ro, ,...,m-1]+ = X-Xn To n