Problem 5 Let 10,11,..., I'm ER be pairwise distinct and let f:R +R be a function. We write pIk. Ik+1,..., for the polynomial of degree l - k that interpolates f at the points #k, Ik+1,..., 21, where k l . Show that P[20, 11, ... , Imre] =P[10, 11, ... , Im-1]+ * (P[11, 11,..., Im] P[70, 11, ... , Im-1]) Problem 5 Let 10,11,..., I'm ER be pairwise distinct and let f:R +R be a function. We write pIk. Ik+1,..., for the polynomial of degree l - k that interpolates f at the points #k, Ik+1,..., 21, where k l . Show that P[20, 11, ... , Imre] =P[10, 11, ... , Im-1]+ * (P[11, 11,..., Im] P[70, 11, ... , Im-1])