Exercise 2.21. Let p(n) be a polynomial function of n. (a) Prove, by induction on d= deg(P), that p(n) can be written as a linear combination of ("+") for j = 0,1,2, ..., d. (b) Briefly explain why there is a polynomial Ap(x) such that p(n)z" Ap(20) (1 - )d+1 n=0 (c) What can you say about the degree of Ap(x)? What can you say about the value of A (1)? Exercise 2.21. Let p(n) be a polynomial function of n. (a) Prove, by induction on d= deg(P), that p(n) can be written as a linear combination of ("+") for j = 0,1,2, ..., d. (b) Briefly explain why there is a polynomial Ap(x) such that p(n)z" Ap(20) (1 - )d+1 n=0 (c) What can you say about the degree of Ap(x)? What can you say about the value of A (1)