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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
If P(2) = 0 for the polynomial P(x) = x^2 - 5x + 6, what can you conclude?
💡 Hint: Identify the root and apply the Factor Theorem.
Question 2
Easy
For the polynomial P(x) = x - 3, what is the factor when P(3) = 0?
💡 Hint: Look for the value of the root.
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 P(a) = 0
- then (x + a) is a factor.
- If P(a) = 0
- then (x - a) is a factor.
- If P(a) ≠ 0
- then (x - a) is a factor.
💡 Hint: Remember the condition of the polynomial when equal to zero.
Question 2
True or False: If x = 3 is a root of P(x), then (x - 3) cannot be a factor.
- True
- False
💡 Hint: Recall the definition from the Factor Theorem.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given P(x) = x^4 - 4x^2 + 4, determine the complete factorization using the Factor Theorem and confirm the factors via computation.
💡 Hint: Apply the Factor Theorem and explore common patterns.
Question 2
For the polynomial P(x) = x^5 - 4x^4 + 6x^3 - 24x^2, find all real factors, utilizing the Factor Theorem effectively.
💡 Hint: Consider grouping for suggested simplifications.
Challenge and get performance evaluation