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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the remainder when dividing 2x^3 + x by x + 1?
💡 Hint: Use synthetic division method.
Question 2
Easy
True or False: All polynomials are reducible.
💡 Hint: Think of irreducible polynomials.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the result when you divide a polynomial by itself?
- Remainder is zero
- The original polynomial
- Quotient is zero
💡 Hint: Remember division properties.
Question 2
True or False: The polynomial x^2 + 1 is irreducible over the real numbers.
- True
- False
💡 Hint: Think about solving for roots.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the polynomial f(x) = x^3 - 7x + 6, determine if it’s irreducible over the rationals.
💡 Hint: Evaluate potential rational roots.
Question 2
Find the GCD of f(x) = x^4 + 2 and g(x) = x^2 + 1 using the Euclidean algorithm.
💡 Hint: Perform polynomial long division.
Challenge and get performance evaluation