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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= + + +
1
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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= +
2
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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= + +
3
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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=
5
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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
6
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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
11
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