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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 of the definition we started with.
Question 2
Easy
What is the factor theorem?
💡 Hint: Recall how roots relate to factors.
Practice 3 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 f(α) = 0
- then (x - α) is a factor of f(x).
- Every polynomial has exactly n factors.
- The degree of a polynomial does not affect the number of roots.
💡 Hint: Think about how roots relate to the factors of polynomials.
Question 2
True or False: A polynomial of degree n can have n distinct roots.
- True
- False
💡 Hint: Recall the relationship between degree and roots.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the polynomial p(x) = 2x^3 - 4x^2 + 2x, find its roots and determine its irreducible components.
💡 Hint: Consider using factoring techniques or the quadratic formula.
Question 2
Factor the polynomial q(x) = x^4 + x² + 1 over complex numbers.
💡 Hint: Look for patterns or potential quadratic factors.
Challenge and get performance evaluation