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Prove that as rings, Z[x]/〈2, x〉 ∼= Z/2. Explain why this proves that 〈2, x〉 is...

Prove that as rings, Z[x]/〈2, x〉 ∼= Z/2.

Explain why this proves that 〈2, x〉 is a maximal ideal in Z[x].

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