1. Algebra II with Trigonometry Ms. Lee
Polynomial Equations
Algebra II with Trigonometry
Ms. Lee

2. Essential Stuff Essential Question Essential Vocabulary
How do you find the zeros of a polynomial function?
Essential Vocabulary
Polynomial Function
Zeros or Root
Rational Root Theorem
Fundamental Theorem of Algebra

3. Solving Equations Methods to solve poly. equations:
Graphing (x-intercepts)
Factoring
Rational Roots
What are some drawbacks to using calculator?

4. Solving by Factoring
The factored form of a polynomial is the product of its linear factors.
What are some forms of factoring that we can use?
Examples of Factored Form

5. Factored Form
A binomial is a factor of a polynomial when the remainder from synthetic division = 0.
Use synthetic division to reduce polynomial to quadratic, and then factor.
Factors from synthetic division and from quadratics give you the factored form of a polynomial.
Examples with given factor

6. Zeros
The zeros of a polynomial are the value(s) of x that make y = 0. When y = 0, the graph intersects the x-axis.
Zeros = roots = x-intercepts
To find zeros, factor polynomial.
How do graphs help us factor polynomials?
What if a polynomial doesn’t factor?

7. Multiple Zeros If a zero is repeated, it is called a multiple zero.
The multiplicity of a zero is the number of times the zero occurs.
Examples Finding Zeros

8. Homework
Homework 6.3