5 Mid-Chapter Quiz

Do you know HOW?

For each polynomial function, describe the end behavior of its graph.

1. f ( x ) = x 8 − 8 x 4 + 6 x 2 f open x close equals , x to the eighth , minus , 8 x to the fourth , plus , 6 x squared
2. f ( x ) = − x 4 − x 3 + 1 f open x close equals negative , x to the fourth , minus , x cubed , plus 1
3. f ( x ) = x 7 − 3 x 5 − 5 x 3 f open x close equals , x to the seventh , minus , 3 x to the fifth , minus , 5 x cubed

4. What is the degree of the function that generates the data shown?

   x	y
   − 3 negative 3	159
   − 2 negative 2	29
   − 1 negative 1	− 1 negative 1
   0	− 3 negative 3
   1	− 1 negative 1
   2	29
   3	159

Find all the solutions of each equation by factoring.

5. x 3 − 5 x 2 = 36 x x cubed , minus , 5 x squared , equals 36 x
6. 27 x 3 = 8 27 x cubed , equals 8
7. x 4 − 20 x 2 + 64 = 0 x to the fourth , minus , 20 x squared , plus 64 equals 0
8. x 3 + 125 = 0 x cubed , plus 125 equals 0
9. Use the Remainder Theorem and synthetic division to find P(4) for P ( x ) = 2 x 4 − 3 x 2 + 4 x − 1 . p open x close equals , 2 x to the fourth , minus , 3 x squared , plus 4 x minus 1 .

You have several boxes with the same dimensions. They have a combined volume of 2 x 4 + 4 x 3 − 18 x 2 − 4 x + 16 . 2 x to the fourth , plus 4 , x cubed , minus 18 , x squared , minus 4 x plus 16 .  Determine whether each binomial below could represent the number of boxes you have.

10. x − 1 x minus , 1
11. x + 2 x plus 2
12. 2 x + 8 2 x plus 8

Write each polynomial in standard form. Then classify it by degree and number of terms.

13. − 2 x 3 + 6 − x 3 + 5 x negative 2 , x cubed , plus 6 minus , x cubed , plus 5 x
14. 3 ( x − 1 ) ( x + 4 ) 3 open x minus 1 close open x plus 4 close

Describe the shape of the graph of each cubic function by determining the end behavior and number of turning points.

15. y = − 5 x 3 y equals negative 5 , x cubed
16. y = 3 x 3 + 4 x 2 + 2 x − 1 y equals , 3 x cubed , plus , 4 x squared , plus 2 x minus 1

Do you UNDERSTAND?

17. You buy one container each of strawberries, blueberries, and cherries. Cherries are $1 more per container than blueberries, which are $1 more per container than strawberries. The product of the 3 individual prices is 5 times the total cost of one container of each fruit.

    1. Write a polynomial function to model the cost of your purchase.
    2. Graph to find the price of each container.
    3. Writing Explain how you used the graph to find the prices.
18. A cylinder has a radius of 3 x − 2 3 x minus 2  and a height of 3 − 2 x . 3 minus 2 x .
    1. Use 3.14 as π pi  and graph the equation for the volume.
    2. Find the relative maximum.
    3. Reasoning What kind of limitation on the radius would make your answer in part (b) the maximum possible volume?
19. Open-Ended Write a polynomial function in factored form with at least three zeros that are negative, one of which has multiplicity 2.

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