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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Evaluate P(3) for the polynomial P(x) = x^2 - 5x + 6.
💡 Hint: Substitute x with 3 and simplify.
Question 2
Easy
Is (x - 1) a factor of x^2 - 3x + 2? Explain why.
💡 Hint: Check if substituting 1 makes the polynomial zero.
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 Factorization Theorem state?
- If P(x) is a polynomial
- then it has a root
- If a linear factor exists
- the polynomial equals zero at that point
- It states nothing about roots
💡 Hint: Think about what happens when substituting the root.
Question 2
True or False: If P(c) != 0, then (x - c) is a factor of the polynomial P(x).
- True
- False
💡 Hint: Remember the definition of factors.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Factor the polynomial P(x) = x^4 - 8x^2 + 16 completely. Identify all roots.
💡 Hint: Recognize it as a quadratic form and take square roots.
Question 2
For P(x) = 3x^3 - 12x^2 + 12x, find all the roots and express in factored form.
💡 Hint: Extract the common factor first, then apply the Factorization Theorem.
Challenge and get performance evaluation