# Advanced Polynomial Functions: Precalculus Lesson Plans Chapter Exam

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### Page 1

#### Question 1 1. Divide using long division.

#### Question 2 2. Divide the following polynomials:

#### Question 3 3. What are the POSSIBLE solutions to the polynomial x^7 - 4x + 3?

#### Question 4 4. Which of the following answer choices is a possible rational zero for the following function?

####
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. Divide the following polynomials:

####
Question 8
8.
Which of the following should be evaluated in order to determine if *x* - 2 is a factor of *x*^3 + 3*x* - 4?

#### Question 9 9. The following graph is of a polynomial function of degree 2. Are the solutions of this function real or imaginary and why?

####
Question 10
10.
According to the Fundamental Theorem of Algebra, the polynomial function *f*(*x*) = *x*^3 + 5*x*^2 - *x* - 5 has how many complex solutions?

### Page 3

####
Question 11
11.
The polynomial *x*^6 + 13*x*^3 + 30 is written in quadratic form as *u*^2 + 13*u* + 30. What does *u* equal?

####
Question 12
12.
Subtract: (*x*2 + 3*x* + 4) - (7*x*2 - 5*x* + 2)

####
Question 13
13.
List the possible rational zeros of the following function:

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

*f*(

*x*) = 6

*x*^3 - 5

*x*- 1

#### Question 14 14. The following graph is of a polynomial function of degree 4. Which of the following best describes the solutions?

####
Question 15
15.
Factor the following expression:

*x*^4 - 13*x*^2 + 36

*x*^4 - 13

*x*^2 + 36

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####
Question 16
16.
Two solutions of the function *f*(*x*) = *x*^3 + 5*x*^2 - 9*x* - 45 are *x* = 3 and *x* = -3. How many solutions and what types of solutions remain?

#### Question 17 17. Divide using long division.

####
Question 18
18.
Divide using synthetic division.

(x3 + 9) / (x + 2)

#### Question 19 19. In the polynomial, 6x^4 - 3x^3 + 3x^2 + 10x + 8, which one is the last constant term?

#### Question 20 20. Divide the following polynomials:

### Page 5

#### Question 21 21. Find the rational solutions to the polynomial x^3 - 2x^2 - x + 2.

#### Question 22 22. Which expression CANNOT be written in quadratic form?

#### Question 23 23. Which example correctly illustrates the Factor Theorem?

####
Question 24
24.
Use the Factor Theorem to determine which expression is a factor of the following polynomial:

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

*f*(

*x*) =

*x*^3 - 2

*x*^2 - 31

*x*- 28.

#### Question 25 25. Divide using long division.

### Page 6

####
Question 26
26.
Write the following expression in quadratic form:

2*x*^6 - 2*x*^3 - 40

*x*^6 - 2

*x*^3 - 40

####
Question 27
27.
Divide using synthetic division.

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

####
Question 28
28.
Divide using synthetic division.

(x3 - 3x2 + 5) / (x - 1)

#### Question 29 29. In this polynomial, 6x^4 - 3x^3 + 3x^2 + 10x + 8, which one is the leading coefficient?

#### Question 30 30. Which of the following is a higher degree polynomial?

#### Advanced Polynomial Functions: Precalculus Lesson Plans 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!