(i) Show, for all a and b and for all j > 1, that ai - b) = (a - b)(a)-1 + a 1-2b + aj-362 + ... + abi–2 + b)–?). (ii) L

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I Show For All A And B And For All J 1 That Ai B A B A 1 A 1 2b Aj 362 Abi 2 B Ii L 1 (26.21 KiB) Viewed 31 times

(i) Show, for all a and b and for all j > 1, that ai - b) = (a - b)(a)-1 + a 1-2b + aj-362 + ... + abi–2 + b)–?). (ii) Let f(x) = Cnx" +Cn-1*"-1 +...+cix+co be a polynomial of degree n. For any number u, show there is some polynomial q(x) of degree n - 1 with f(x) = (x – u)q(x) + f(u). (Hint: n n n f(x) = f(u) = { c;x- Ücju' = Ï ¢} (x) – w'); j=0 j=0 j=0 now use part (i).]