4 Let F be a eld a Let f x 6 Mr and a 6 IF Prove that x a divides x f a b Suppose that a m f L b g m 1 where a 3 b a f x
Let F be a eld a Let f x Mr and a IF Prove that x a divides x f a b Suppose that a m f L b g
Let F be a eld a Let f x Mr and a IF Prove that x a divides x f a b
f x Mr and a IF Prove that x a divides x f a b Suppose that a m f L b g m where a b a f x
Let F be a eld a Let f x Mr and a IF Prove that x a divides x
f a b Suppose that a m f L b g m where a b a f x
Let F be a eld a Let f x Mr and a IF Prove that
Let F be a eld a Let
4' Let F be a eld. (a) Let f(x) 6 Mr] and a 6 IF. Prove that x a divides x) f(a). (b) Suppose that a(m)f(:L') + b($)g(m) = 1 where a(3:),b(a:),f(x)...

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Im having trouble on how to show that x-a divides f(x)-f(a) do i need to show that a is a root of f(x)-f(a)? ATTACHMENT PREVIEW Download attachment Screen Shot 2017-11-22 at 7.19.05 PM.png 4‘ Let F be a ?eld. (a) Let f(x) 6 Mr] and a 6 IF. Prove that x — a divides ?x) — f(a). (b) Suppose that a(m)f(:L') + b($)g(m) = 1 where a(3:),b(a:),f(x) and g(a.r:) are polynomials over IF. Prove that f (x) and 9(1') do not have any roots in common.

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