Divide \( x^4 \) by \( x^2 \) to get \( x^2 \).
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- A quantum computing cryptography expert is working on a protocol that involves calculating the remainder when \( x^4 + 3x^2 + 1 \) is divided by \( x^2 + 1 \). What is the remainder?
- To find the remainder when \( x^4 + 3x^2 + 1 \) is divided by \( x^2 + 1 \), we perform polynomial long division.
- Divide the leading terms:
- Multiply and subtract:
- Multiply \( x^2 \) by \( x^2 + 1 \) to get \( x^4 + x^2 \).
- Subtract from the original polynomial:
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