Algebra II Practice Test Intro. and Graphing Polynomials Unit 4 Part I

Name__________________________________________ Period__________ Date________________

NON-CALCULATOR SECTION

Vocabulary: Define each word and give an example.

1. Polynomial Function

2. Multiplicity

3. Local Maximum

Short Answer:

4. What is the Remainder Theorem?

5. What is the 6th row of Pascal’s Triangle?

Review:

6. Solve the equation. Check your solution(s):

7. What is the discriminant of the quadratic equation ? Describe what it means if the discriminant is negative, positive, or zero.

8. Write an equation in standard form for the line perpendicular to that passes through

the point .

Algebra II Practice Test Intro. and Graphing Polynomials Unit 4 Part I

9. Simplify:

Problems: **Be sure to show all work used to obtain your answer. Circle or box in the final answer.**

10.

Complete the chart.

11. Perform the indicated operation:

a. b.

c. d.

12. Use long division: 13. Use synthetic division:

divided by

Example Degree Name by degree No. of terms Name by # of terms

5x + 353 4 2x x

3x

x4+3 x2+6 x+1

Algebra II Practice Test Intro. and Graphing Polynomials Unit 4 Part I

14. Factor the polynomial:

a. b. c.

15. Use synthetic substitution to evaluate the polynomial function at .

16. Determine if is a factor of without dividing.

17. Describe the end behavior of the polynomial function f ( x )→__________ as x→−∞

. f ( x )→__________ as x→∞

18. State the degree and list the zeros of the polynomial function. State the multiplicity of each zero and whether the graph crosses the x-axis at the corresponding x-intercept. Then, sketch the graph of the

polynomial function by hand.

degree =_____________

zeros, multiplicity and whether it crosses:

__________________________________________

__________________________________________

__________________________________________

19. Graph the polynomial functions.

a. b.

-4 -2 2 4

-20-15-10-5

5101520253035404550

x

y

Algebra II Practice Test Intro. and Graphing Polynomials Unit 4 Part I

MULTIPLE CHOICE QUESTIONS

20. Factor the polynomial completely.

A.

B.

C.

D.

21. According to the Remainder Theorem, which of the following is the remainder when the polynomial

is divided by ?

A.B.C.D.

22. Which of the following describes the end behavior of the graph of as ?

A.

B.

C.

-4 -2 2 4

-20

-15

-10

-5

5

10

15

20

x

y

-4 -2 2 4

-10

-5

5

10

x

y

Algebra II Practice Test Intro. and Graphing Polynomials Unit 4 Part I

D.

23. A pyramid-shaped sculpture has a volume of 18 cubic inches. The length of a side of the square base of the pyramid is 3 inches less than the height of the pyramid. What equation could model this situation?

Recall:

A.

B.

C.

D.

Name__________________________________________ Period__________ Date________________

CALCULATOR SECTION

1. a) Expand . b) Expand .

2. Find the seventh term of the binomial expansion .

3. Find the coefficient of the term with in the expansion of .

4. Graph the function in your calculator:

Algebra II Practice Test Intro. and Graphing Polynomials Unit 4 Part I

a. Approximate the real zeros of .

b. What is the local maximum of ?

c. What is the local minimum of ?

d. Using interval notation, where is the function increasing?

e. Using interval notation, where is the function decreasing?