I am working on Exercise 8 of Dummit and Foote Section 9.2 Exercise 8

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Determine the greatest common divisor of and in

and write it as a linear combination (in ) of a(x) and b(x).

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In working on this I applied the Division Algorithm to a(x) and b(x) resulting in

then

Last non-zero remainder is -3

Therefore, gcd is -3

BUT!

This does not seem to be correct because -3 does not divide either a(x) and b(x)

Can someone please help?

Peter