Trashketball Review

Chapter 6

Polynomial Functions and Stuff

Trashketball Review of ch 3

11

2

34

78

6

5 10

12

11

9

16

15

1413

20

191817

21 2622

232425

2

+/-1, +/-2, +/-5, +/-10,

+/- ½, +/- 5/2

1052)(

zeros rational possible all Find2 xxxf

3

F(x) =

4Using your TI-83, identify the x-intercepts, local max and local min of the graph of

X-int: (0, -3) and (0, 3)

5

)3)(1)(4(

operation thePerform

xxx

12133 xx

6

FACTOR

7

Solve

8Find all of the zeros of the function below:

9Simplify

10Create a function for the following end behavior.

The function must be of degree 5 or higher and the function must have at least 5 terms.

Answers will vary but MUST be correct to get

credit.

11Use synthetic division to determine if 2 is a zero of f(x) = 2x3 – 3x2 – 6x + 6. And EXPLAIN how you know.

No.

f(2) has a remainder

of -2

12 Suppose a polynomial function of degree 5 with rational coefficients has the

given zeros: -3, , and 4+3i. Find the other zeros.

iand 342

13Use synthetic substitution to

find the function value f(-10) if

220,141)10( f

f(x) = x5 – 4x4 + x3 – x2 + 2x - 100

14 Consider the graph the polynomial function: f(x) = 3x(x + 5)(x – 4)(x + 1)(x – 2):

a) What are the zeros of the function? b) What are the x-intercepts of the function? c) What is the degree of this function?

a) 0, -5, 4, -1, 2

b) (0,0), (-5,0) , (4,0), (-1,0) , (2,0)

c) 5th degree

15

Use synthetic division to find the quotient (x4 - 6x2 + 5) ÷ (x + 3)

x3 – 3x2 + 3x – 9 +

16Find ALL zeros of the function

f(x) = x4 + x3 – 7x2 – x + 6

2, 1, -1, -3

17Find a polynomial of lowest degree with rational coefficients that has the given numbers as some of its zeros:

3, 2 – 5i

87417)( 23 xxxxf

18Mathematically describe the end behaviors for the function below:f(x) = 6x3 – 2x2 – 5x8 + 3x - 9

Must have both parts correct:

)(,

)(,

xfxAs

xfxAs

19List all possible rational zeros of the function

f(x) = 9x3 – 5x2 + x – 12

9

4,

9

2,

9

1,

3

4,

3

2,

3

1

,12,6,4,3,2,1

20 Simplify

21Multiply: (x+3)(x+2)(x-1)

X3 + 4x2 + x - 6

g(x) =

22

For 1990 to 1998, the value of a horse winning

the Kentucky Derby can be modeled by:

V = 2553x3 – 25200.56x2 + 64026.95x + 428075.56

Where x is the number of years since 1990. Use a graphing calculator to determine what year the winnings were $488,150

23There are seven teams in the Atlantic Division of the Eastern Conference of the NBA. During the 1997-98 season the winning percentage of teams in this division can be modeled by:

W = -0.0051x3 + 0.063x2 – 0.260x + 0.862

Where x is the team’s ranking within the division. Orlando’s winning percent was 0.500. Use the graphing calculator to estimate their ranking in the division.

5

24Write a cubic function that passes through the given points:(-1,0), (2,0), (3,0),(0,9)

f(x) = 3/2 (x+1)(x-2)(x-3)

25Factor:x4 - 16

(x2 + 4)(x + 2)(x – 2)

26Solve:x3 + 4x2 = 7x + 28