PreCalculus: Lesson Plan * 10/06/2006

Quickstart
1. Find all the zeros of f(x) = 6x⁴ - 33x³ - 18x².
2. Determine the right-hand and left-hand behavior of f(x) = 6x⁴ - 33x³ - 18x².
3. Find a polynomial function of degree 3 that has zeros of 0, 2, and -1/3

Lesson
(2.3) Real Zeros of Polynomial Functions
Objective: Students will know how to use long division and synthetic division to divide polynomials by other polynomials, determine the number of zeros of a polynomial, and find real zeros of polynomial function.

I. Long Division

The Division Algorithm



II. Synthetic Division


III. Remainder and Factor Theorems

Remainder Theorem



Factor Theorem



IV. The Rational Zero Test