FTCE Middle Grades Mathematics 5-9 (025): Practice & Study Guide  /  Math Courses

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FTCE Middle Grades Math: Polynomial Functions Chapter Exam

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!

Page 1

Question 1 1. Use the Remainder Theorem to find the remainder when f(x) = x^4 + 4x^3 - x^2 - 16x -12 is divided by x - 4.

Question 2 2. Two solutions of the function f(x) = x^3 + 5x^2 - 9x - 45 are x = 3 and x = -3. How many solutions and what types of solutions remain?

Question 3 3.

Divide using synthetic division.

(x4 + 5x3 - 15x2 - 12x - 60) / (x - 3)

Question 4 4. What is the leading coefficient of this function: y = x^3 - 2x^4 + 1

Question 5 5. Which answer choice is not a possible rational zero for the following function?

Page 2

Question 6 6. The following graph is of a polynomial function of degree 2. Are the solutions of this function real or imaginary and why?

Question 7 7.

Write the following expression in quadratic form:

2x^6 - 2x^3 - 40

Question 8 8. A polynomial function has real coefficients, a leading coefficient of 1, and the zeros 3 - i, 3 + i, 4, and 4. Write the polynomial function in factored form.

Question 9 9.

Factor the following expression:

x^8 + 8x^4 + 15

Question 10 10. Which example correctly illustrates the Remainder Theorem?

Page 3

Question 11 11. A polynomial function has real coefficients, a leading coefficient of 1, and the zeros 8, -i and i. Write a polynomial function of least degree in standard form.

Question 12 12. All polynomial graphs must:

Question 13 13. What is the degree of this function: y = 3x^2 - 4x^5 + x - 1.

Question 14 14.

Use the Factor Theorem to determine which expression is a factor of the following polynomial:

f(x) = x^3 - 2x^2 - 31x - 28.

Question 15 15. What happens to the graph of a function when it is made negative?

Page 4

Question 16 16. Divide using long division.

Question 17 17.

List the possible rational zeros of the following function:

f(x) = 6x^3 - 5x - 1

Question 18 18.

Divide using synthetic division.

(2x3 + 5x2 - 9) / (x + 1)

Question 19 19. Which of the following should be evaluated in order to determine if x - 2 is a factor of x^3 + 3x - 4?

Question 20 20. Divide using long division.

Page 5

Question 21 21. What does 'Evaluating Polynomials in Function Notation' really mean?

Question 22 22. Divide using long division.

Question 23 23. The factored form of a polynomial function is f(x) = (x + 4)(x - 2)(x - 1)(x + 1). According to the Fundamental Theorem of Algebra, what is the degree of this function?

Question 24 24. What transformation to the graph occurs when f(x) = x^2 is changed to f(x) = 3(x-2)^2?

Question 25 25. How will the graph of f(x)=x^3 transform when changed to f(x) = x^3 - 5?

Page 6

Question 26 26. A polynomial function has real coefficients, a leading coefficient of 1, and the zeros -4i and 4i. Write a polynomial function of least degree in standard form.

Question 27 27. A polynomial function has real coefficients, a leading coefficient of 1, and the zeros -6, 1, and 1. Write a polynomial function of least degree in standard form.

Question 28 28. How can you tell if a graph is from an Odd Degree Polynomial function?

Question 29 29. The possible rational zeros for the following function are +/-1 and +/-2. Which synthetic division problem shows that 2 is NOT a rational zero of the function?

Question 30 30.

Divide using synthetic division.

(x2 + x - 20) / (x + 5)

FTCE Middle Grades Math: Polynomial Functions 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!

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