MHB F[x]: Congruence Solutions | Math Q&A

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Hi all, I have completed this question as attached. Hope someone could help to check if my solutions are correct. However, I am not sure what theorem is used for part (d). May need some advice. Thanks.
 

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All your solutions look correct. (Yes)

Just a minor comment, but you might want to put the equivalence class brackets around the terms belonging to $R$.
 

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