1. Real Zeros
Intro - Chapter 4.2

2. Rational Zeros
The Rational Root Theorem
Let P be a polynomial function with integer coefficients in standard form.
If _______ (a reduced fraction ) is a _______ of
then
ROOT
p is a factor of the ______________ term of P.
CONSTANT
q is a factor of the ________________________ of P
LEADING COEFFICIENT

3. Completely Factored Polynomials
Example 4: Factor f(x) completely.
Step 1: List all ____________ rational roots.
POSSIBLE
Step 2: ________and choose
the best rational
root from your list.
GRAPH
Looks like -3 or 1/2

4. Step 3: Use _____________ division to find all
_____________ factors.
SYNTHETIC
RATIONAL

5. Step 4: Find all ________________ zeros using the
_________________________
IRRATIONAL
QUADRATIC EQUATION
Step 5: Write in _____________ form.
FACTORED

7. Example 1: List all of the possible rational roots of
q = ____
Factors of p = _________________
Factors of q = _________________
All possible rational roots of f(x) are