Let A be the integers modulo 7.(adsbygoogle = window.adsbygoogle || []).push({});

b(x)= x^3 -2 and c(x) = x^3 + 2 are polynomials in A[x].

How can you show that A/<b(x)> and A/<c(x)> have the same number of elements? In this practice problem I already showed that A/<b(x)> and A/<c(x)> are fields by showing that <b(x)> and <c(x)> are maximal ideals, but I don't know how this helps.

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# Polynomial factor rings

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