1. Title of Lesson: Real Zeros of Polynomials

2. By the end of this lesson, I will be able to answer the following questions… 1. How do I use long division and synthetic division to divide polynomials and use those results to discover roots of the polynomial? 2. What is the remainder theorem and how do I use it in conjunction with the factor theorem to break down polynomials? 3.How do I use the rational zero test and/or a graphing calculator to discover roots of polynomials that are not easily factored.

3. Vocabulary 1. The division algorithm: 2. f(x) is the dividend. 3. d(x) is the divisor. 4. q(x) is the quotient. 5. r(x) is the remainder.

4. Prerequisite Skills with Practice Graph Use the graph to predict what the factors of f(x) would look like. A polynomial has the zeros x=2/3, x=0 and x=-4/5. Find a polynomial that fits this description

5. Long Division of Polynomials Long Division of Polynomials

6. Synthetic Division.

7. The Remainder Theorem: If a polynomial f(x) is divided By (x-k), then the remainder is R=f(k) The Factor Theorem: A polynomial f(x) has a factor (x-k) if and only if f(k)=0 Use the remainder to evaluate the following function at x=-2 Show that (x-2) and (x+3) are factors of

8. Dr. Fitz-whiskers has discovered a box of DEATH! However, if he can find the volume of the box of DEATH(!) then he will be rewarded the golden magic super- terrific hamster wheel of pure bliss. The volume of the box in the polynomial form is Dr. Fitz-whiskers has the following clues…. 1.The height of the box is 25 inches. 2.A width of the box can be is (x-5) inches 3.The height of the box is greater than it’s length. (don’t use your calc or the box of DEATH(!) will automatically activate.)

9. Homework: 3,5,6,8,9,15,19,20,21,36,37,(43-48) all (61-64) all (87-90) all 93 97,98