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Abstract Algebra, Euclidean Algorithm

  • Thread starter kuahji
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Use the Euclidean Algorithm to find the gcd of the given polynomials:

(x3-ix2+4x-4i)/(x2+1) in C[x]

First I got x-i R: 3x-3i, then I took the 3x-3i into x2+1 & got 1/3 x R: 1+i. Then I was going to take 1+i into 3x-3i. However that never ends it seems, unless I just confused myself.

The answer in the back of the book is just x-i for the gcd. So I'm thinking I should have stopped earlier, & believe I'm just over looking something simple. Any suggestions?
 

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