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MATH3066 (ND) 2025 MATH3066 Exam Practice Multiple Choice Questions D

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Consider the field 𝑅 = 𝑍 2 [ 𝑥 ] / 𝐼 where 𝐼 = ( 𝑥 4 + 𝑥 3 + 𝑥 2 + 𝑥 + 1 ) 𝑍 2 [ 𝑥 ] . Find 𝛼 − 1 ∈ 𝑅 where 𝛼 = 𝐼 + 𝑥 + 1 .

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