20.2 - Addition and Multiplication of Polynomials Over Fields
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Practice Questions
Test your understanding with targeted questions
Define irreducible polynomial in simple terms.
💡 Hint: Think about what would happen if we could break it down.
In GF(5), what would be the result of adding (3x + 4) and (2x + 2)?
💡 Hint: Be careful with adding coefficients!
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the result of adding 2x^2 + 2 and x^2 + 1 in GF(3)?
💡 Hint: Remember to add coefficients considering modulo.
True or False: The product of any two non-zero elements in a field cannot be zero.
💡 Hint: Recall the definition of field behavior.
1 more question available
Challenge Problems
Push your limits with advanced challenges
If f(x) = x^4 + 1 and g(x) = x^2 + 2, determine their GCD over GF(5).
💡 Hint: Start by dividing the higher degree polynomial.
Prove that (x - 3) is a factor of f(x) = x^3 - 9 in GF(10).
💡 Hint: Check for roots directly in the polynomial.
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