Polynomial Functions

f(x)=ax(^n) +bx(^n-1) +cx(^n-2)

 

Is it a factor?

Yes --- when your remainder is zero

 

Find a factor of polynomial functions:

- long division

- synthetic division

 

Remainders written as:

 answer + (remainder/what you divided by)

 

 

 

Long Division

Is x-2 a factor of  ?

 

 

  

The remainder is zero, therefore yes.

 

Is x+3 a factor of  ?

 

 

Synthetic Division-if the coefficient is 1 and with no exponets

1. Take opposite of dividend and place in box

2. write coefficient of equation following the box

3. Bring down the first term

4. Multiply by what is in the box

5. Add and repeat

6. Start with first number of exponet is one less than original equation

7. Include remainder properly

 

Is x-2 a factor of  ?

 

 2l 1 -4 2       

1  2 4

     2 -2 6

 

the answer is 2x-2 with a remainder of 6

 

Rational Root Test

-Making a list of all possible rational roots

 

p:factors of last terms

q:all factors of the first term

 

 Ex:

p: 1, 11     Possible Rational Roots:

q: 1, 2       + 1, + 1, + 11, + 11

                     1     2      1       2

no rational roots

 

TO DO:

-Make possible rational roots list

-Check answers on calculator

-Zeros on the graph are the rational roots

 

*The # of answers is the # of exponents on the 1st term