chapter 1 - polynomial final exam review.docx

8/10/2019 Chapter 1 - Polynomial Final Exam Review.docx

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Final Exam Review Questions

Chapter 1 - Polynomial Functions

1. How many of the following functions represent polynomial functions.

I.

( )1

3 25 4f x x x= +

II.

( ) 2 12 3f x x x=

III.

( ) 4 3 2!"2! 1 4#5f x x x x= + +

I$.

( ) 3 25 3 2 4f x x x x= +

$.

( ) 3 1xf x = +

$I.

( ) 21 52f x x x= +

a% 2 &% 3 c% 4 '% all

2. (etermine the )alue of ain

( ) 3 2 5P x x ax x= + + +

if

( )2 3P =

.

a% -2 &% 3 c% 2 '% -3

3. In the partially complete' synthetic 'i)ision &elow* a polynomial

( )P x

is 'i)i'e' &y2.x

1 -2 # 3

1 " # 15

+he 'i)ision statement* e,presse' in

P DQ R= +

* that &est represents the a&o)e synthetic'i)ision is

a%

( ) ( )( )3 22 2 # 3P x x x x= + +

&%

( ) ( )( )3 22 2 # 3 15P x x x x x= + + +

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c%

( ) ( ) ( )2 # 15P x x x= + +

'%

( ) ( )( )22 # 15P x x x= + +

4. hen the polynomial

32 #a a +is 'i)i'e' &y

4a * the remain'er is/

a% -!4 &% 1" c% ## '% 1"#

5. (etermine one factor the following polynomial

4 3 2 #y x x x x= + +

a%

( )2x +

&%

( )3x +

c%

( )3x

'%

( )#x

#. 0ne factor of

3 2# 23 # x x x+ is

4x +. +he other two factors are

a%2 1 an' 3 2x x +

&%2 1 an' 3 2x x+

c% # 1 an' 2x x+

'%# 1 an' 2x x +

. If -2* "* an' 4 are the only eros of a fourth 'egree polynomial function*

( )P x

* which of the

following is a possi&le factore' form of

( )P x

a%( ) ( ) ( )2 4P x x x x

= +

&%

( ) ( ) ( )2 2

2 4P x x x x= +

c%

( ) ( ) ( )2# 2 4P x x x x= +

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'%

( ) ( ) ( )4 2 4P x x x x= +

. hich of the following is nota polynomial function

a%

3 25 3 # 3y x x x= + &%

2# 5 4y x x= +

c%

( ) ( )3

3 2g x x x= +

'%

( ) 4 1f t t=

!. hich of the following coul' not&e a polynomial function

a% &%

c% '%

1". hich function correspon's to the graph to the right

a%

( ) 3 24 3f x x x= + +

&%

( ) 4 3 22 g x x x x x= + +

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c%

( ) 3 22 ! #h x x x x= +

'%

( ) 4 3 23 3j x x x x x= +

11. hich of the following is the in)erse of

( ) 3 23f x x x= +

a% &%

c% '%

12. hat is the euation of the in)erse of

3 21 15 2

2 4y x x x= + +

a%

3 21 12 45 2

y x x x= +

&%

3 21 15 22 4

y x x x= +

c%

3 21 15 22 4

x y y y= + +

'%

3 2

1

1 15 2

2 4

y

x x

=

+ +

13. hat is the greatest num&er of real roots that

3 2 45 3 2 #x x x x = +

can ha)e

a% 2 &% 3 c% 4 '% 5

4


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14. hich cu&ic function has eros of

1* 1* 4

a%

( ) ( )4 1 4y x x= +

&%

( ) ( )2

5 1 4y x x= +

c%

( ) ( )2

1 4y x x= +

'%

( ) ( )2

2 1 4y x x= +

15. hich uartic function has eros of3* 1* 2* 4

a%

( ) ( ) ( ) ( )2 3 1 2 4y x x x x= + +

&%

( ) ( ) ( )4 3 1 2y x x x= + +

c%

( ) ( ) ( ) ( ) 3 1 2 4y x x x x=

'%

( ) ( ) ( ) ( )5 3 1 2 4y x x x x= + +

1#. hat is the euation of the cu&ic function

shown on the graph at the right

a%

( ) ( )2

2 1 3y x x= + +

&%

( ) ( )2

3 1 3y x x=

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c%

( ) ( )1 3y x x x= +

'%

( ) ( )2

2 1 3y x x= +

1. hat is the euation of the uartic function

shown on the graph at the right

a%

( ) ( ) ( )21

3 1 23

y x x x= + +

&%

( ) ( ) ( )2

2 2 1 3y x x x= +

c%

( ) ( ) ( )2

2 1 3 2y x x x= +

'%

( ) ( ) ( )1 3 2y x x x x= + +

1. hich of the following represents the graph of

( ) ( )2 3 4y x x x= +

a% &%

c% '%

1!. hich euation represents the cu&ic function with eros

3* 2* #

an' a

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y-intercept of1

a%

( ) ( ) ( )1

# 2 32

y x x x= + +

&%

( ) ( ) ( )1

# 2 32

y x x x= +

c%

( ) ( ) ( )# 2 3 54y x x x= + +

'%

( ) ( ) ( )1

# 2 32

y x x x= +

2". ol)e

3 25 4 "x x x =

a%

2* "* 2

5

&%

22* "*

5

c%

5* "* 2

2

'%

52* "*

2

21. How many of the following functions are notpolynomial functions

i%

( ) 3 2 3 5 !f x x x x= +

ii%

( ) 2 # 2f x x x= +

iii%

( ) ( )2 3 5y x x x= +

i)%

4 23 5

2 3 12y x x= +

)%( )

2

3

x x

f x x

+

=

)i%

23 5 2y x x= +

a% 2 &% 3 c% 4 '% #

22. hich of the following graphs coul' &e the graph of the polynomial functi

( ) ( ) ( )2

if "* "* an' "P x c x a x b a b c= + + < > 1* &> -2

32. a>3* &>2* c>1

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chapter 1 - polynomial final exam review.docx

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