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Unformatted text preview: particular in section 9.1, have a look at the example involving long division in Z 5 on page 231, and see the Remainder Theorem 9.12 and the Factor Theorem 9.14 on page 232, and in section 9.9, look at example 9.92 on page 260. It is also worth noticing that Theorem 9.17 in section 9.1 does not always hold for polynomials over Z n . (a) Solve x 2 + 3 x + 2 ≡ 0 (mod 6), then ﬁnd two diﬀerent ways to factor the polynomial f ( x ) = x 2 + [3] x + [2] over Z 6 . (b) Solve x 2 +2 x +26 ≡ 0 (mod 125), then ﬁnd two diﬀerent ways to factor the polynomial f ( x ) = x 2 + [2] x + [26] over Z 125 ....
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This note was uploaded on 07/25/2011 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.
 Spring '08
 ANDREWCHILDS
 Algebra, Congruence

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