Do A/<b(x)> and A/<c(x)> have the same number of elements?

[bigreddog]

Let A be the integers modulo 7.
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.

 

[mathwonk]

you stated it wrong it seems. you want A[x]/<whatever>. then it gets easier.