1. Rational Root Theorem
Math 3
MM3A1

2. To find the zeroes of a Polynomial:
The Rational Root Theorem:
If f(x) = anxn a1x + a0 has integer coefficients, then every rational zero of f(x) has the following form: p =
factor of constant term a0 q
factor of leading coefficient an

3. Use the rational root theorem to determine all possible rational roots:
What is the constant?
-10
This is going to be the numerator
What is the leading coefficient? 2
This is going to be the denominator
Possible roots:

4. Things to consider:
The degree of the polynomial will tell you the max number of zeroes
Some roots may be imaginary
Use factors of the constant term (a0) as your numerator
Use factors of the leading coefficient (an) as your denominator
Use your calculator and synthetic division to determine if the possible ratios are actual zeroes

5. Find the rational zeroes of:
Possible:
Use your calculator to graph the function and determine which possible zeroes to try.
Which ones look like they may work?
Use synthetic division to check them

6. Actual Solutions 2 -3/2 1/4 Try 2 2 8 -6 -23 6
now use, the smaller polynomial:
Try -3/2
-3/
-12 3 2
-3/2
1/4
Actual Solutions

7. Now, you can give the factored form of the equation
The zeroes for
are { 2, -3/2, ¼ }
So, the factored form of the equation is:

8. Find the rational zeroes of:
Possible:
Use your calculator to graph the function and determine which possible zeroes to try.
Which ones look like they may work?
Use synthetic division to check them

9. Actual Solutions 3 -3/2 1/3 Try 3 3 6 -11 -24 9
now use, the smaller polynomial:
Try -3/2
-3/
-9 3 3
-3/2
1/3
Actual Solutions

10. Now, you can give the factored form of the equation
The zeroes for
are { 3, -3/2, 1/3 }
So, the factored form of the equation is: