general

Polynomial Functions

I. Graph f(x)=-x(2-x)3(x-3)2

A. The intercepts are

Y Intercept: x=0

Y=0(2-0)3(0-3)2

Y= 0

II. X intercept: y=0

0=-x(2-x)3(x-3)2

-x=0

Dividing both sides by -1 gives

X=0

Hence (0,0)

B. Degree of Polynomial

F(x)=-x1(2-x)3(x-3)2

Add all the powers to obtain the degree of the function

1+2+3=6; Therefore,

= 6th degree function

C. Give each Zero and its Multiplicity

(2-x)3 ……..+1 {invert the signs to the opposite to obtain the zeros}

(x-3)2…………….+3

-2x+x2……………-1

III. Multiplicity

To obtain the multiplicity count the number of powers above the zeros

ie, -x1(2-x)3(x-3)2

Here there are 3 so the multiplicity, M=3

D. Behavior of the Function

Y=0

-1 3

X=0