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