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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the remainder when \(P(x) = x^2 + x - 6\) is divided by \(x - 3\)?
💡 Hint: Use the Remainder Theorem and substitute \\(x = 3\\).
Question 2
Easy
Calculate the remainder when \(P(x) = x^3 + 2x + 1\) is divided by \(x + 1\).
💡 Hint: Evaluate 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 Remainder Theorem help to calculate?
- Remainder of polynomial division
- Sum of polynomial terms
- Degree of a polynomial
💡 Hint: Think about what the theorem states regarding division.
Question 2
T/F: The remainder can be found by substituting the linear divisor's root into the polynomial.
- True
- False
💡 Hint: Recall the theorem's statement about division.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that if \(P(x) = x^4 - 5x^3 + 6x^2\) has a remainder of \(0\) when divided by \(x - 3\), that \(x - 3\) is a factor.
💡 Hint: Don't forget to substitute \\(3\\) into \\(P(x)\\).
Question 2
Given \(P(x) \) is divided by \(x - 1\), find \(P(x)\) for it to yield a remainder of \(4\). Write a polynomial.
💡 Hint: Incorporate any polynomial as \\(Q(x)\\) such that this holds true.
Challenge and get performance evaluation