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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify the root of f(x) = x - 3.
💡 Hint: What value makes f(x) equal to 0?
Question 2
Easy
What defines a monic polynomial?
💡 Hint: Consider the highest degree term.
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
A polynomial of degree n can have at most how many roots?
- n-1
- n
- n+1
💡 Hint: Consider how roots relate to the degree.
Question 2
True or False: Every polynomial has at least one real root.
- True
- False
💡 Hint: Think about polynomials with even degrees and positive leading coefficients.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Factor the polynomial f(x) = x^4 - 5x^2 + 6.
💡 Hint: Try substituting a new variable to simplify the expression.
Question 2
Prove that the polynomial x^5 + x + 1 has no rational roots.
💡 Hint: Evaluate potential candidates and see if f(α) = 0 is ever true for them.
Challenge and get performance evaluation