1. Polynomials and Linear Factors
Algebra II with Trigonometry
Mrs. Agnew

2. Essential Stuff Essential Question Essential Vocabulary
How do you find the zeros of a polynomial function?
Essential Vocabulary
Linear Factor
Extrema
Zero or Root

3. Factored Form
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

4. Zeros of Polynomials
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.

5. 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 of finding zeros…

6. Writing Polynomial Functions
If given the zeros of a polynomial, we can write a function.
Create the binomial factor that corresponds to each zero, then multiply.
Examples

7. What if? What if a polynomial doesn’t factor?
Does that mean it doesn’t have zeros?

8. Homework:
Page 144 #42-48 (even), 50, 52, 54, 60 Page 145 # (Find the zeros)