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Home » \( n = 1 \) works. - Esdistancia

\( n = 1 \) works. - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 v^4 + 3v + 1 = (v^2 + 1)Q(v) + R(v),

📌 where \( R(v) \) is the remainder and has degree less than 2, so let \( R(v) = av + b \).

📌 Divide the leading term \( v^4 \) by \( v^2 \), giving \( v^2 \).

📌 Multiply \( v^2(v^2 + 1) = v^4 + v^2 \).

📌 Subtract: \( (v^4 + 3v + 1) - (v^4 + v^2) = -v^2 + 3v + 1 \).

📌 Divide \( -v^2 \) by \( v^2 \), giving \(-1\).

📌 Multiply: \(-1(v^2 + 1) = -v^2 - 1\).

📌 Subtract: \((-v^2 + 3v + 1) - (-v^2 - 1) = 3v + 2\).

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