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Homework Statement
(A somewhat similar question to my last one). Let [itex]J[/itex] be the ideal of the polynomial ring [itex]\mathbb{Q}[x][/itex] generated by [itex]x^2 + x + 3[/itex]. Find the multiplicative inverse of [itex](3x^3 + 3x^2 + 2x -1) + J[/itex] in [itex]\mathbb{Q}[x]/J[/itex]
Homework Equations
The Attempt at a Solution
I think I need to apply the extended Euclidean algorithm to 3x^3 + 3x^2 + 2x -1 and x^2 + x + 3 in order to find the greatest common divisor, but I am unsure of the details. Also, once I find the gcd, I don't know what I'm supposed to do with it.