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

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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)?
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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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