math iv - worksheet polynomial functions 2

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Math IV: Advanced Algebra & Trigonometry

ID: 1

Name___________________________________

Date________________K p290G1o2h LKqu0t9aC gS1opfetIwwahrveK ALPLlCB.v X xAhlOl3 YrRixgeh4tcsP ar8etsre0rOvGeJd5.1Worksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x

x

x

2)

f (

x)

x

x

x

x 3)

f (

x)

x

x

4)

f (

x)

x

x

x

x 5)

f (

x)

x

x

x

State the possible rational zeros for each polynomial function. Then find all zeros.

6)

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x)

x

x

x

x

x 7)

f (

x)

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

x

10)

f (

x)

x

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x

x

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x

x

x

x 15)

f (

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Answers to Worksheet: Polynomial Functions 2 (ID: 1)1) Possible # positive real zeros: 0

Possible # negative real zeros: 5, 3, or 12) Possible # positive real zeros: 2 or 0

Possible # negative real zeros: 2 or 03) Possible # positive real zeros: 1

Possible # negative real zeros: 04) Possible # positive real zeros: 2 or 0

Possible # negative real zeros: 2 or 05) Possible # positive real zeros: 2 or 0

Possible # negative real zeros: 2 or 06) Possible rational zeros:

, , , , , , , Zeros:

, ,

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Zeros: , , 8) Possible rational zeros:

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,

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9) Possible rational zeros: , Zeros: , ,

10) Possible rational zeros: , , , , , Zeros:

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11) Possible rational zeros: , Zeros:

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12) Possible rational zeros: , , ,

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13) Possible rational zeros: , , , Zeros: ,

14) Possible rational zeros: , , , , , , , , , Zeros:

,

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ID: 2

Name___________________________________

Date________________D t2w0f1u2O 7KDuItkaq 8SxoBfWtNwqaVraeJ nLwLWCq.5 m LAHlTlV qrHiIgbhvtXsm 8ryeLs8eErYv2ecd6.SWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x 2)

f (

x)

x

x

x

3)

f (

x)

x

x

x

x

x

4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x

x 7)

f (

x)

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x

x

x

x 11)

f (

x)

x

x

x

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x

x 15)

f (

x)

x

x

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Possible # negative real zeros: 4, 2, or 04) Possible # positive real zeros: 4, 2, or 0

Possible # negative real zeros: 15) Possible # positive real zeros: 1

Possible # negative real zeros: 4, 2, or 06) Possible rational zeros: , , ,

Zeros:

,

i,

i7) Possible rational zeros: , ,

Zeros: , , , 8) Possible rational zeros: ,

Zeros: , 9) Possible rational zeros:

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10) Possible rational zeros: , , , , ,

Zeros: , i, i, i, i11) Possible rational zeros:

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,

i ,

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Zeros: , 13) Possible rational zeros: ,

Zeros:

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i14) Possible rational zeros: , , ,

Zeros:

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,


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i ,

i

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ID: 3

Name___________________________________

Date________________f l2y08182c NKHuBt4aT 5SCokfVtEw7axr8eK DL6LoC5.J t jAilulR 3rLiSg0hCtusW 2rSe2slelrmvJe4da.fWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x 2)

f (

x)

x

x

x

3)

f (

x)

x

x

x

x

x

4)

f (

x)

x

x 5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x 7)

f (

x)

x

x

x

8)

f (

x)

x

x

x 9)

f (

x)

x

x

x

x

x

10)

f (

x)

x

x

x 11)

f (

x)

x

x

x

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

x

x

14)

f (

x)

x

x 15)

f (

x)

x

x

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Possible # negative real zeros: 2 or 03) Possible # positive real zeros: 5, 3, or 1



Possible # negative real zeros: 4, 2, or 06) Possible rational zeros:

, , , , , , , Zeros:

i ,

i ,

i ,


, , , , , Zeros:

,

,

8) Possible rational zeros: , Zeros: mult. 2,


,

i ,

i ,

i ,


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,

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i11) Possible rational zeros:

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,

i ,

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i ,

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12) Possible rational zeros: , , , Zeros:

,

,

i ,

i

13) Possible rational zeros: , , , , , , , , , Zeros:

,

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ID: 4

Name___________________________________

Date________________v R2g0D1h2Q SKouqtYaF HSDoUfotTwGawrmeV uLoL7CU.J F AArlhll orWiug4hltNsA ErweUsAeXrNvVeZdb.dWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x 2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x

x 4)

f (

x)

x

x

x

x

x

5)

f (

x)

x


6)

f (

x)

x

x 7)

f (

x)

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

x

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

x

x

14)

f (

x)

x

x

x

x

x 15)

f (

x)

x

x

x

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Answers to Worksheet: Polynomial Functions 2 (ID: 4)1) Possible # positive real zeros: 2 or 0





Possible # negative real zeros: 16) Possible rational zeros: , , ,

Zeros:

,


Zeros: mult. 2, 8) Possible rational zeros: ,

Zeros: , 9) Possible rational zeros: , , ,

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i,

i10) Possible rational zeros: ,

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i, i,

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i

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,

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ID: 5

Name___________________________________

Date________________j w2e0p1c2f rKLu3tKam QSMo5fwtuwzarr5eL YLvLRC7.i Z vA6l5lz GrIi5gThNt3sl prueZsweCrkvaejdW.ZWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

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x)

x 2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x

x

4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x

x 7)

f (

x)

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

x

12)

f (

x)

x

x

x

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x 15)

f (

x)

x

x

x

x

x

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Possible # negative real zeros: 16) Possible rational zeros: ,

Zeros:

,

,

7) Possible rational zeros:

, , , , , , , Zeros:

,

i,

i


,


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i ,

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,


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,

,

12) Possible rational zeros: , Zeros: , i mult. 2, i mult. 2


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Zeros:

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i ,

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ID: 6

Name___________________________________

Date________________I 0290h1j2h BKJuxt6ab OSEoefFtYwka4raew YLcL5CC.Y G RA8l1lq CrkivgchdtRsY PrDeIsreXrPv5exdI.KWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x

x

x

2)

f (

x)

x

x

x

x

x

3)

f (

x)

x 4)

f (

x)

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x

x 7)

f (

x)

x

x

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

x

10)

f (

x)

x

x

x

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

14)

f (

x)

x

x 15)

f (

x)

x

x

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Answers to Worksheet: Polynomial Functions 2 (ID: 6)1) Possible # positive real zeros: 4, 2, or 0





Possible # negative real zeros: 4, 2, or 06) Possible rational zeros: ,

Zeros: , mult. 27) Possible rational zeros:

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, ,


,

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12) Possible rational zeros: , , , , Zeros:

,

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13) Possible rational zeros: ,

Zeros: mult. 2, 14) Possible rational zeros: , , , , ,


Zeros:

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ID: 7

Name___________________________________

Date________________Q a20031H2Q oKxuPtOag JSJoHfvt7wta2reeI 1LVL5CK.m K 1AMldl6 YrriAg3hVt7sh VrOenseeZrdv4ezdo.HWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x 4)

f (

x)

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x 7)

f (

x)

x

x

x

8)

f (

x)

x

x

x

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x

x

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x

x

x

x 15)

f (

x)

x

x

x

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i,


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15) Possible rational zeros: , ,

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,

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ID: 8

Name___________________________________

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1)

f (

x)

x

x

x

x

x 2)

f (

x)

x

x

x

3)

f (

x)

x 4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x

x

x

x 7)

f (

x)

x

x

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

14)

f (

x)

x

x 15)

f (

x)

x

x

x

x

x

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Possible # negative real zeros: 14) Possible # positive real zeros: 4, 2, or 0



Zeros:

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,

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i mult. 28) Possible rational zeros: ,


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ID: 9

Name___________________________________

Date________________K 82B0l1Y21 jKEuetyaa USWoHfStgwkadrKeA TLRLOCD.D g iAnlslM PrEiUgPhutOsl 0r5ePszeFr4vIesdI.yWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x

x

x 2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x 4)

f (

x)

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x 7)

f (

x)

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x

x 11)

f (

x)

x

x

x

12)

f (

x)

x 13)

f (

x)

x

x

x

x

x

14)

f (

x)

x

x

x

x

x 15)

f (

x)

x

x

x

x

x

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Possible # negative real zeros: 16) Possible rational zeros:

Zeros: , , i, i7) Possible rational zeros: ,

Zeros:

i,



Zeros:

i, i,

i ,


Zeros: mult. 2, 11) Possible rational zeros:

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,

,


,

,

i ,

i

13) Possible rational zeros: , , , Zeros: , i, i, i, i


,

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i , i, i

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ID: 10

Name___________________________________

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1)

f (

x)

x 2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x

x

x

x 4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x


6)

f (

x)

x

x

x 7)

f (

x)

x

x

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

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ID: 11

Name___________________________________

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ID: 12

Name___________________________________

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ID: 13

Name___________________________________

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ID: 14

Name___________________________________

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Possible # negative real zeros: 5, 3, or 13) Possible # positive real zeros: 1




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ID: 15

Name___________________________________

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ID: 16

Name___________________________________

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ID: 17

Name___________________________________

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ID: 18

Name___________________________________

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ID: 19

Name___________________________________

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ID: 20

Name___________________________________

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ID: 21

Name___________________________________

Date________________U H2W011T2K wKluft7af pSqoXfRtQwzaOrzeu aLALtCO.K 0 NAYldlS MrOidgKhBtusU ZrkeosVecr9viehdE.KWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x 2)

f (

x)

x

x

3)

f (

x)

x

x

x

x

x

4)

f (

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x

x

x

x

x

5)

f (

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x

x

x

x


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x

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x 7)

f (

x)

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x

x

x

x

8)

f (

x)

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x 9)

f (

x)

x

x

10)

f (

x)

x

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

14)

f (

x)

x

x

x 15)

f (

x)

x

x

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Possible # negative real zeros: 4, 2, or 06) Possible rational zeros: , , ,

Zeros:

, ,

, i, i7) Possible rational zeros: , ,

Zeros:

, i, i,

i ,



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i,


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,


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ID: 22

Name___________________________________

Date________________F h2r081I2U cK4uPt5aM YS8oNf7tWwkaVrCe6 sLQL6Cv.G j BARlQla lrkirg8hvtbsU Crfebsne0rsvce5d9.fWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x

x

x 2)

f (

x)

x

x

x

x

x

3)

f (

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x

x 4)

f (

x)

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x

x

x

x 7)

f (

x)

x

x

x

8)

f (

x)

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x 9)

f (

x)

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x

x

10)

f (

x)

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x

x

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x 15)

f (

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x

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, , , , , Zeros:

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ID: 23

Name___________________________________

Date________________m 92P0K1m2s PKFu9tOap 7SKovfctHwwakroeG ELQLTCS.J l RAclNl0 DrTiagbhJt9s3 FrjensheerXvceLd8.UWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

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x)

x

x

x

x

x 2)

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x

x

x

x

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f (

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x

x

5)

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x

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x

x


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f (

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f (

x)

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x

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x)

x

x 9)

f (

x)

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x

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f (

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f (

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x

x

x

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12)

f (

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x

x

x

x

x 13)

f (

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x

x

14)

f (

x)

x

x 15)

f (

x)

x

x

x

x

x

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ID: 24

Name___________________________________

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f (

x)

x 2)

f (

x)

x

x

x

x

x

3)

f (

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x

x

x

x

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f (

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x

x

x

5)

f (

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x

x

x


6)

f (

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x

x

x

x 7)

f (

x)

x

x

x

x

x

8)

f (

x)

x

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f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

x

x

14)

f (

x)

x

x

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x

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ID: 25

Name___________________________________

Date________________8 T2X0v1l2g yKHuptFa5 VSYo5fztDwDaMrteQ mLQLiCb.z c VABlfl8 erwipgqhKtZs0 YrVePs8eSr1v8eedr.UWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

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f (

x)

x

x 2)

f (

x)

x

x

x

x

3)

f (

x)

x

x

x

4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x

x


6)

f (

x)

x

x 7)

f (

x)

x

x

8)

f (

x)

x

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

x

x

x

12)

f (

x)

x

x

x 13)

f (

x)

x

x

x

14)

f (

x)

x

x 15)

f (

x)

x

x

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Zeros:

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ID: 26

Name___________________________________

Date________________n g2l001t2x 8KtuntiaM rSHoDfntfwYaWrweQ xL8LgCb.i l YA5l6l7 RrziIgghrtPsn 3rBeqsQeUrbvGeodt.rWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

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f (

x)

x 2)

f (

x)

x

x

x

3)

f (

x)

x

x

x

x

x

4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x

x

x

x 7)

f (

x)

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

x

10)

f (

x)

x

x

x

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x

x

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x

x 15)

f (

x)

x

x

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Possible # negative real zeros: 16) Possible rational zeros: , , , ,

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Zeros: mult. 2, 8) Possible rational zeros: , , ,

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,

,

i ,



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ID: 27

Name___________________________________

Date________________5 g2e0V1u2p rKJuMtoaK 2SjoYfztzwmaUrVep ULJLgC0.N M tAElflP urOiQgvhStXsy brWeFsje9rfvdeWdB.5Worksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x 2)

f (

x)

x

x

x

3)

f (

x)

x

x

x 4)

f (

x)

x

x

x

5)

f (

x)

x

x

x

x


6)

f (

x)

x

x 7)

f (

x)

x

x

x

x

x

8)

f (

x)

x

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x

x

x

x 11)

f (

x)

x

x

12)

f (

x)

x

x 13)

f (

x)

x

14)

f (

x)

x

x 15)

f (

x)

x

x

x

x

x

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Possible # negative real zeros: 2 or 06) Possible rational zeros: ,

Zeros:

i,

i7) Possible rational zeros: , , , , ,

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,

i ,

i ,

i ,


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,

i,


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ID: 28

Name___________________________________

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1)

f (

x)

x

x

x

x

x 2)

f (

x)

x

3)

f (

x)

x

x 4)

f (

x)

x

x

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x 7)

f (

x)

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

x

x

x

10)

f (

x)

x 11)

f (

x)

x

x

12)

f (

x)

x 13)

f (

x)

x

x

x

14)

f (

x)

x

x

x

x

x 15)

f (

x)

x

x

x

x

x

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Zeros: mult. 2, 7) Possible rational zeros: ,


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ID: 29

Name___________________________________

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1)

f (

x)

x

x

x

2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x

x

x

x

4)

f (

x)

x

x 5)

f (

x)

x

x

x


6)

f (

x)

x

x

x 7)

f (

x)

x

x

x

x

x

8)

f (

x)

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x 11)

f (

x)

x

x

x

x

x

12)

f (

x)

x

x

x 13)

f (

x)

x

x

14)

f (

x)

x

x

x

x

x 15)

f (

x)

x

x

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Possible # negative real zeros: 2 or 06) Possible rational zeros: , ,

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,

,


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13) Possible rational zeros: , , , ,

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,


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ID: 30

Name___________________________________

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1)

f (

x)

x

x

x

x

x

2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x

4)

f (

x)

x

x

x

x

x

5)

f (

x)

x


6)

f (

x)

x

x 7)

f (

x)

x

x

8)

f (

x)

x

x

x

x

x 9)

f (

x)

x

x

10)

f (

x)

x

x

x 11)

f (

x)

x

x

x

x

x

12)

f (

x)

x

x 13)

f (

x)

x

x

x

x

x

14)

f (

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x

x 15)

f (

x)

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x

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, ,

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ID: 31

Name___________________________________

Date________________A l220e1224 dKEuNtEao OS9oJfmtLwZazrleM 8LRLsC3.x h PALlil9 kr3iogthWtqsf Erye4sAePrdvPe0dI.WWorksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

1)

f (

x)

x

x

x

x

x 2)

f (

x)

x

x

x

x

x

3)

f (

x)

x

x

x 4)

f (

x)

x

x

x

5)

f (

x)

x

x

x

x

x


6)

f (

x)

x

x 7)

f (

x)

x

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ID: 32

Name___________________________________

Date________________N A2Q0J1W2e CKLultaak TS4ozf9tdwRa6rAel RLvLlCn.d r 1Aklelj 7rVimgrhLtCsY SryersLe3rkvXehdo.9Worksheet: Polynomial Functions 2State the possible number of positive and negative real zeros for each function.

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math iv - worksheet polynomial functions 2

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