Section 5.1

Polynomial Functionsand Models

OBJECTIVE 1

( ) ( )

( ) ( )

( ) ( ) ( )

5 4 3 2

133

2

(a) 3 4 2 5 (b) 3 5 10

(c) 3 5 (d) 2 3 8

(e) 5 (f) 3 2 1

f x x x x g x x x

h x x F x x x

G x H s s s

−

= − + + = + −

= − = + −

= − = −

Summary of the Properties of the Graphs of Polynomial Functions

OBJECTIVE 2

5Graph: 2 x+

( )4Graph: - 2 1x +

OBJECTIVE 3

Find a polynomial of degree 3 whose zeros are -4, -2, and 3.

( ) ( ) ( )3 44 2f x x x= + −

For the polynomial, list all zeros and their multiplicities.

( ) ( ) ( )23For the polynomial 3 2f x x x x= − − +

OBJECTIVE 4

( ) ( ) ( )( )2Analyze the graph of the polynomial function 4 1 2f x x x x= + + −

( ) 3 2

Analyze the graph of the polynomial function 3.12 3.512 5.1354f x x x x= − − + −

OBJECTIVE 5