xFall Chapter 8 Day #7 ­ The Rational Root Theorem (8.3.2) Notes.notebook
December 02, 2016
Chapter 8
Day #7
Rational Root Theorem
Section 8.3.2
Objectives:
Students will....
1. Determine possible rational roots of a polynomial.
2. Use the Rational Root Theorem to find all roots of a polynomial function. 1
xFall Chapter 8 Day #7 ­ The Rational Root Theorem (8.3.2) Notes.notebook
December 02, 2016
Consider: Factorization:
Roots:
How do we get the leading coefficient?
How do we get the constant?
How do these numbers compare to the roots?
root = 2
xFall Chapter 8 Day #7 ­ The Rational Root Theorem (8.3.2) Notes.notebook
December 02, 2016
Rational Root Theorem
If a polynomial has a rational root, then it will occur at p/q, where p is a factor of the constant and q is a factor of the leading coefficient. List all Possible Roots:
Ex1:
Ex2:
3
xFall Chapter 8 Day #7 ­ The Rational Root Theorem (8.3.2) Notes.notebook
December 02, 2016
Finding All the Roots of a Polynomial:
a. How many total roots are there, counting multiplicities?
b. What are all the possible rational roots?
c. Using you graphing calculator, identify the actual rational roots.
d. Use synthetic division to compress the polynomial and then solve to find the remaining roots.
e. Write the polynomial in factored form.
Finding All the Roots of a Polynomial:
a. How many total roots are there, counting multiplicities?
b. What are all the possible rational roots?
c. Using you graphing calculator, identify the actual rational roots.
d. Use synthetic division to compress the polynomial and then solve to find the remaining roots.
e. Write the polynomial in factored form.
4