# Understanding Polynomial Functions Chapter Exam

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### Page 1

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Question 1
1.
Factor the following expression:

*x*^8 + 8*x*^4 + 15

*x*^8 + 8

*x*^4 + 15

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

#### Question 3 3. Which of the following shows the graph of the equation below?

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Question 4
4.
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?

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Question 5
5.
Subtract: (*x*3 + *x*3 + 6) - (*x*3 - 2*x* + 1)

### Page 2

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Question 6
6.
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 7 7. Divide using long division.

#### Question 8 8. The following graph is of a polynomial function of degree 2. Are the solutions of this function real or imaginary and why?

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Question 9
9.
Multiply: (*x* + 1)(*x* + 6)

#### Question 10 10. What is the degree of this function: y = 3x^2 - 4x^5 + x - 1.

### Page 3

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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. Which of these statements is true about adding polynomials?

#### Question 13 13. What is the short run behavior of this graph?

#### Question 14 14. All polynomial graphs must:

#### Question 15 15. How will the graph of f(x)=x^3 transform when changed to f(x) = x^3 - 5?

### Page 4

#### Question 16 16. Which of the following shows the graph of the equation below?

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Question 17
17.
Use the Remainder Theorem to find the remainder when *f*(*x*) = *x*^4 + 4*x*^3 - *x*^2 - 16*x* -12 is divided by *x* - 4.

#### Question 18 18. What happens to the graph of a function when it is made negative?

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Question 19
19.
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 20 20. Which of the following shows the graph of the equation below?

### Page 5

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Question 21
21.
Solve for z.

x + z = 2

#### Question 22 22. Where do you look for the long run behavior?

#### Question 23 23. What is the long run behavior of this graph?

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Question 24
24.
Add: (*x*2 + 5*x* + 2) + (*x*2 - 2*x* + 7)

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Question 25
25.
What does x equal when y = 3?

x + y = 8

### Page 6

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

#### Question 27 27. Which of the following shows the graph of the equation below?

#### Question 28 28. Which of the following shows the graph of the equation below?

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Question 29
29.
Divide using synthetic division.

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

#### Question 30 30. Which example correctly illustrates the Remainder Theorem?

#### Understanding 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!