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FTCE Mathematics 6-12 (026): Practice & Study Guide  /  Math Courses

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FTCE Math: Polynomials 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. Which of the following is the correct expansion of the expression below?

Question 2 2. 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 3 3.

Divide using synthetic division.

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

Question 4 4. What happens to the graph of a function when it is made negative?

Question 5 5.

Divide using synthetic division.

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

Page 2

Question 6 6. Which example correctly illustrates the Remainder Theorem?

Question 7 7. All polynomial graphs must:

Question 8 8. What is the leading coefficient of this function: y = x^3 - 2x^4 + 1

Question 9 9. 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 10 10. Divide using long division.

Page 3

Question 11 11. Which expression CANNOT be written in quadratic form?

Question 12 12. What does a negative leading coefficient do to a graph?

Question 13 13. Given f(x) = x^2 + 3x -2; find f(3).

Question 14 14. What transformation to the graph occurs when f(x) = x^2 is changed to f(x) = 3(x-2)^2?

Question 15 15.

List the possible rational zeros of the following function:

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

Page 4

Question 16 16. Which example correctly illustrates the Factor Theorem?

Question 17 17.

Write the following expression in quadratic form:

2x^6 - 2x^3 - 40

Question 18 18. What is the degree of this function: y = 3x^2 - 4x^5 + x - 1.

Question 19 19. The graph of the function f(x) = x^3 - 4x^2 - 2x + 8 is shown below. This function has only one rational zero. Use the rational zeros theorem and the graph to determine the value of the rational zero.

Question 20 20. To what does 'Polynomial Graph Transformation' refer?

Page 5

Question 21 21. Which of the following lists of numbers shows the coefficients for (x + 1)4 using Pascal's triangle?

Question 22 22. According to the Fundamental Theorem of Algebra, the polynomial function f(x) = x^3 + 5x^2 - x - 5 has how many complex solutions?

Question 23 23. 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 24 24. The polynomial x^6 + 13x^3 + 30 is written in quadratic form as u^2 + 13u + 30. What does u equal?

Question 25 25. How do you say f(5)?

Page 6

Question 26 26. What does 'Polynomial' mean?

Question 27 27.

Divide using synthetic division.

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

Question 28 28. Divide using long division.

Question 29 29. What does 'Evaluating Polynomials in Function Notation' really mean?

Question 30 30. 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?

FTCE Math: 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!

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