20 - Polynomials Over Fields and Properties
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Practice Questions
Test your understanding with targeted questions
What is the remainder when dividing 2x^3 + x by x + 1?
💡 Hint: Use synthetic division method.
True or False: All polynomials are reducible.
💡 Hint: Think of irreducible polynomials.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the result when you divide a polynomial by itself?
💡 Hint: Remember division properties.
True or False: The polynomial x^2 + 1 is irreducible over the real numbers.
💡 Hint: Think about solving for roots.
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Challenge Problems
Push your limits with advanced challenges
Given the polynomial f(x) = x^3 - 7x + 6, determine if it’s irreducible over the rationals.
💡 Hint: Evaluate potential rational roots.
Find the GCD of f(x) = x^4 + 2 and g(x) = x^2 + 1 using the Euclidean algorithm.
💡 Hint: Perform polynomial long division.
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Reference links
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