Let f(x) = x^2 + ax + b ∈ F3[X]. What is the number of non-isomorphic quotient rings F3[X]/(f(X))? F3 is a field with 3 elements.
Added by Laura O.
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We are given a polynomial \(f(x) = x^2 + ax + b\) in the polynomial ring \(F_3[X]\), where \(F_3\) is the field with 3 elements (0, 1, 2). We need to find the number of non-isomorphic quotient rings of the form \(F_3[X]/(f(X))\). Show more…
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