1. Bellwork
Write the equation of the graph below in factored form.

2. Bell work Identify the type of polynomial
Identify the number of solutions
Identify the type of solutions (Classify)

3. 7.5 Zeros of Polynomial Functions
Students will be able to:
Use the Rational Root Theorem and the Complex Conjugate Root Theorem to find the zeros of a polynomial function.
Use the Fundamental Theorem to write a polynomial function given sufficient information about its zeros.

4. Rules and Properties Complex Conjugate Theorem
7.5 Zeros of Polynomial Functions
Rules and Properties
Complex Conjugate Theorem
If P is a polynomial function with real-number coefficients
and a + bi is a root (zero).
then a – bi is also a root (zero).

5. Rules and Properties Rational Root Theorem
7.5 Zeros of Polynomial Functions
Rules and Properties
Rational Root Theorem
P is a polynomial function with integer coefficients.
If is a root of P(x) = 0, then p q
p is a factor of the constant term of P.
q is a factor of the leading coefficient of P.

6. Example 1
Using the Rational Root Theorem, list all the POSSIBLE roots of the polynomial below.

7. Problem 1
Using the Rational Root Theorem, list all the POSSIBLE roots of each polynomial below.

8. Problem 3
Find all roots to the polynomial equation below.

9. 7.5 Zeros of Polynomial Functions
Problem 2
Write the equation for a third degree polynomial whose zeros are listed below and P(0) = -6 in factored & standard form.

10. 7.5 Zeros of Polynomial Functions
Example 2
Write the equation for a third degree polynomial whose zeros are 2 and i and P(0) = 4 in both factored & standard form.

11. Problem 4
According to the Fundamental Theorem of Algebra, what can I conclude about the polynomial below?
2. Given -6 as a root of the polynomial above, find the remaining roots.

12. Homework
7.5: P even, odd, 41-43all, 47 (graphing calculator, synthetic division and factoring. You must show work.
Test Tuesday- We have a no calc portion.