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F_2[x]/(x^3+x+1)is a field, but F_3[x]/(x^3+x+1) is not a field; it’s not even an integral domain. Explain...

F_2[x]/(x^3+x+1)is a field, but F_3[x]/(x^3+x+1) is not a field; it’s not even an integral domain. Explain why (hint: as an analogy, recall Z/7Z is a field but Z/6Z is not a field; it’s not even an integral domain.

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