HN Math III: Unit 3 – POLYNOMIAL TEST REVIEW Name ______________________________

1. Look at the graphs below and answer the following:

a) What is the degree? b) How many zeros does the function have? c) Describe the end behavior d) State the interval(s) where the function is increasing e) Circle any extrema

2. Which polynomial function has zeros at 5, –4, and –3 ?

a. c.

b. d.

3. Find the zeros of and state the multiplicity.

a. –2, multiplicity 6; 4, multiplicity –3

b. –2, multiplicity 6; –3, multiplicity 4

c. 6, multiplicity –2; –3, multiplicity 4

d. 6, multiplicity –2; 4, multiplicity –3

4. Divide by x + 2.

a. c.

b. , R –29 d. , R 23

5. Divide

a. c.

b. d.

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6. Find the zeros of . Then graph the equation.

a. 5, 2, –5

c. 5, 2

b. 0, 5, 2

d. 0, –5, –2

7. Determine which binomial is a factor of .

a. x + 5 b. x + 20 c. x – 24 d. x – 5

Find the roots of the polynomial equation

8.

a. –3 ± 5i, –4 c. –3 ± i, 4

b. 3 ± 5i, –4 d. 3 ± i, 4

9.

a. c.

b. d.

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

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HN Math III: Unit 3

POLYNOMIAL REVIEW

1. Complete the table below

Function Degree Highest possible # of Max & Mins

End Behavior

A 𝑓(𝑥) = 3𝑥 − 𝑥 0

B 𝑔(𝑥) = −𝑥 + 5𝑥 + 3

C ℎ(𝑥) = 3(𝑥 + 2)(𝑥 − 4)

D 𝑗(𝑥) = −2𝑥 − 𝑥 + 5𝑥 − 1

2. Evaluate the polynomial 𝑓(𝑥) = 3𝑥 − 𝑥 + 6𝑥 − 𝑥 + 1 for 𝑥 = −2. Explain what your answer represents.

3. Find the zeros for the function 𝑓(𝑥) = 𝑥 + 3𝑥 − 𝑥 − 3

4. Show whether -4 is a zero of 𝑔(𝑥) = 𝑥 − 𝑥 − 14𝑥 + 24

5. Use the graph to answer the following questions

a) Relative maximum:

b) Relative minimum:

c) Increasing interval:

d) Decreasing interval:

e) Domain:

f) Range:

g) End Behavior:

h) Zeros:

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no D

C N D

x soo y a

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Find all the zeros:

6. 𝑓(𝑥) = 2𝑥 + 3𝑥 − 39𝑥 − 20 7. 𝑓(𝑥) = 𝑥 + 6𝑥 − 7

Divide using long division:

8. 𝑥 − 3𝑥 + 8𝑥 − 5 ÷ (𝑥 − 1) 9. 4𝑥 − 12𝑥 − 𝑥 + 15 ÷ (2𝑥 − 3)

10. Sketch a graph:

𝑓(𝑥) = −4(𝑥 − 1) (𝑥 − 3)(𝑥 + 8)

12. A cement walk of uniform width surrounds a rectangular swimming pool that is 10 m wide and 50 m long. Find the width of the walk if its area is 864 m2.

13. The number of eggs, f(x), in a female moth is a function of her abdominal width, x, in millimeters, modeled by f(x) = 14x3 – 17x2 – 16x + 34. What is the abdominal width when there are 211 eggs?

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Lx i x

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zx

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6 2 10

g 21 0 4 2 120 86446.5346 0 6 30 216

211 14 3 17 2 16 340 14 3 17 2 16 177

x

Complete the following table

2. The following table gives a ticket price a theater can charge and the profit they can expect to see over the course of a year. Use successive differences to determine the best model to fit this data and then find the model using technology.

3. The total number of video cassettes sold from 1995 to 2005 at Bob’s store can be modeled by the function F(x) = 4x3+14x2+200x+1560 and the number of kinds of video cassettes in Bob’s store from 1995 to 2005 can be modeled by G(x) = 2x + 12, where x is the number of years since 1995. Using division, find the average number of each kind of video cassettes that Bob sold.

X 5 3 x 4

x 7 x 19 3 1

Xt x 74 2 Xt 3 xxx 2

ll ll l

z ll l3 5

yquadratic

7.44 a 2 y 0000374 24.06 537.247 187 06 l8

12327 2

21 1 6

6J 4 14 200 1560I 24 60 15604 10 260 Le4 2 10 260 X 5 130

2

HN Math III: Unit 3

GRAPHING POLYNOMIALS MATCHING REVIEW Directions: Complete the chart below with information about the degree, leading coefficient, and end behavior of the function. Then use the graphs included on the next page to match the graph with its corresponding polynomial function.