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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Evaluate f(3) for f(x) = x^2 - 9 before identifying a factor.
💡 Hint: Plug in x = 3 into the polynomial.
Question 2
Easy
Check if (x - 1) is a factor of f(x) = x^2 - x.
💡 Hint: Evaluate f(x) at x = 1.
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 about a polynomial and its value at a root?
- The polynomial is always positive
- It has a factor
- It cannot be evaluated
💡 Hint: Remember what happens at roots.
Question 2
If f(0) = 5, does (x - 0) divide the polynomial f?
- True
- False
💡 Hint: Consider how factors relate to roots.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if a polynomial of degree n has n distinct roots, then it can be expressed as a product of linear factors.
💡 Hint: Break down the proof by induction over the degree.
Question 2
Given a polynomial p(x) = x^4 - 16, find its factors and confirm the roots using the Factor Theorem.
💡 Hint: Consider how to approach factorization in steps.
Challenge and get performance evaluation