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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a root of a polynomial?
💡 Hint: Think about what happens when you substitute a number into the polynomial.
Question 2
Easy
Define a monic polynomial.
💡 Hint: What is special about the leading coefficient?
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 does the factor theorem state?
- If α is a root
- then (x - α) is a factor.
- All roots are irrational.
- Polynomials cannot have real coefficients.
💡 Hint: Think about what happens if substituting α into the polynomial results in zero.
Question 2
True or False: A polynomial of degree n can have at most n roots.
- True
- False
💡 Hint: Relate to polynomial properties.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the polynomial x^5 + x^3 + x^2, find its irreducible factors over the field of integers.
💡 Hint: Look for integers that satisfy the equation.
Question 2
Using the polynomial x^4 + 2x^2 + 1, identify and justify its potential irreducibility.
💡 Hint: Check if your polynomial resembles the form of squares.
Challenge and get performance evaluation