1. Finding Zeros of Polynomials
Honors Precalculus
February 22-23, 2018
Mr. Agnew

2. Essential Stuff Essential Question
How do you find the zeros of a polynomial?
Essential Vocabulary
Zero
Degree
Rational Root
Sythetic Division

3. Remainder & Factor Theorems
The Remainder Theorem
Given polynomial P(x), the value of P(c) is remainder from synthetic division using c.
If you get a remainder of zero when using c in the “box,” what can you say about c?
If c is a zero of function, then x – c is a factor of polynomial.
Examples…

4. Rational Root Theorem
Given a polynomial of degree n with integer coefficients,
The Rational Root Theorem
Potential zeros can be found by putting the factors of the constant term over the factors of the coefficient of the leading term.
Use synthetic division to determine which potential zero is in fact a zero.

5. Zeros of Polynomials Steps to find the zeros of a polynomial:
Find possible rational zeros (calculator)
Use a rational zero and synthetic division to reduce polynomial
Repeat until polynomial is reduced to quadratic
Solve quadratic
*A rational zero may be used more than once in synthetic division.
Practice: pg 209 #40, 46, 68, 80, 96 ; pg 216 #34, 40

6. Homework
page 209 – 210
#41, 47, 49, 53, 55, 65, 69, 79, 81, 85, 95