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