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Long division

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Let p(x) = x 3 + x + 1, and q(x) = x 2 + x. Perform long division of p, by q, in the following fields. (I.e. write p(x) = f(x)q(x) + r(x) where degr < degq.) (a) F = R (b) F = Z3 (Hint: Use (a).) (c) F = Z5 (Hint: Use (a).)

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