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For each of the following pairs of polynomials f(x) and g(x), write f(x) in the form...

For each of the following pairs of polynomials f(x) and g(x), write f(x) in the form
f(x) = k(x)g(x) + r(x)
with deg(r(x)) < deg(g(x)).

a)   f(x) = x^4 + x^3 + x^2 + x + 1 and g(x) = x^2 − 2x + 1.
b)   f(x) = x^3 + x^2 + 1 and g(x) = x^2 − 5x + 6.
c)   f(x) = x^22 − 1 and g(x) = x^5 − 1.

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