# Roots & Coefficients of Polynomials Chapter Exam

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#### Question 1 1. If there are 6 solutions, how many intervals are there?

#### Question 2 2. For the polynomial function f(x) = (x - 1)(x - 2)(x + 3), how many positive intervals are there?

#### Question 3 3. Which of the following polynomials has these intervals: (negative infinity, -6), (-6, 2), (2, 3), (3, positive infinity)?

#### Question 4 4. If a certain function produces -36 as an answer for the x value of 5, which of the following intervals is most definitely negative?

#### Question 5 5. How many intervals does the function f(x) = x have?

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#### Question 6 6. Make a list of the possible solutions for this polynomial.

#### Question 7 7. The numerator of our possible solutions from the rational roots theorem comes from which term in our polynomial?

#### Question 8 8. Which of the following is a possible solution to this polynomial?

#### Question 9 9. Which of the following statements is true?

#### Question 10 10. Which of the following is a solution to this polynomial?

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Question 11
11.
Fill in the blank: If the factor (*x* - *a*)*n* shows up in the complete factorization of a polynomial, then the multiplicity of *a* is _____.

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Question 12
12.
Consider the completely factored polynomial *P* = (*x* - 5)2 (*x* + 1)(*x* + 7)3. What is the multiplicity of the root -7?

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Question 13
13.
Given the completely factorized polynomial *P* = (*x* + 2)(*x* - 9)4 (*x* - 14), what are the roots of *P*?

#### Question 14 14. The graph of a polynomial is shown. Based on the graph, which of the following statements is true?

#### Question 15 15. Which of the following statements is NOT true?

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#### Question 16 16. If the roots of a polynomial are 2, 4 and -5, what are the factors?

#### Question 17 17. How many roots would the following polynomial have?

#### Question 18 18. Write a polynomial with roots 1, -1 and 3.

#### Question 19 19. Write a polynomial with roots of 1, 2 and -2.

#### Question 20 20. Write the factors of the polynomial with roots, 3, -3 and 6.

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#### Question 21 21. Use Newton's method to find the root of f(x), starting at x=2.

#### Question 22 22. You would like to use Newton's method to find the root of f(x). What is the equation you will need to solve?

#### Question 23 23. Use Newton's method to find the root of f(x), starting at x=1.

#### Question 24 24. Use Newton's method to find the root of f(x), starting at x=1.

#### Question 25 25. You would like to use Newton's method to find the root of f(x). What is the equation you will need to solve?

#### Roots & Coefficients of Polynomials Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!