2.6%20Find%20Rational%20Zeros

1
2.6 Find Rational Zeros

• Pg. 89

2
Long Division
Synthetic Division
3
Synthetic Division
4
Synthetic Division
Cant be done!!!
5
Synthetic Division
6
Factoring a Polynomial

• Factor
  given that (x 3) is a factor

7
Finding Zeros of a Function

• Find the other zeros of
  given that 1 is a zero.

Zeros! Roots! Solutions!
All of these mean to solve for x!
8
2.6Find Rational Zeros

• Polynomial TEST Friday

9
History Lesson!

• Find all real zeros of f(x) x3 7x2 14x 8

10
Example

• Find all real zeros of f(x) 6x3 17x2 4x 3

Use graph to confirm one root from the list.
Which one?
Do synthetic then solve the quadratic.
11
Example

• Find all real zeros of f(x) x3 8x2 16x 5

Use graph to confirm one root from the list.
Which one?
Do synthetic then solve the quadratic.
12
(No Transcript)
13
2.8 Analyze Graphs of Polynomial Functions
Multiplicity
14
Repeated Zeros of a Polynomial
Multiplicity of
1
15
Repeated Zeros of a Polynomial
Multiplicity of
2
16
Repeated Zeros of a Polynomial
Multiplicity of
3
17
End behavior
18
Factoring a Polynomial by Using Its Graph
Give a possible factorization of the following
polynomials. Do NOT multiply out the factors!
Be sure to use your knowledge of the Leading
Coefficient Test and Repeated Zeros.
19
Factoring a Polynomial by Using Its Graph
Give a possible factorization of the following
polynomials. Do NOT multiply out the factors!
Be sure to use your knowledge of the Leading
Coefficient Test and Repeated Zeros.
20
Homework

• Pg. 91, 5 14 all
• Pg. 92, 1 10 all