1. Objectives Identify the multiplicity of roots Use the Rational Root Theorem and the Irrational Root Theorem to solve polynomial equations

2.  As with some quadratic equations, factoring a polynomial equation is one way to find its real roots  Factoring Polynomials in Quadratic Form (Degree 4 or Higher) ◦ Follow previous factoring rules ◦ Remember rules of exponents when creating binomials  Recall the Zero Product Property ◦ You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x

5.  You can use a graphing calculator to see roots  You cannot always determine the multiplicity of a roots from a graph.  It is easiest to determine multiplicity when the polynomial is in factored form.  If you can’t factor, use synthetic division to help you.  Get the root for synthetic from the graphing calculator

6.  x 3 + 6x 2 + 12x + 8 = 0  x 4 + 8x 3 + 18x 2 – 27 = 0  x 4 – 8x 3 + 24x 2 – 32x + 16 = 0

7.  Not all polynomials are factorable, but the Rational Root Theorem can help you find all possible rational roots of a polynomial equation. ◦ Also known as the “p over q” theorem

9.  The design of a box specifies that its length is 4 inches greater than its width. The height is 1 inch less than the width. The volume of the box is 12 cubic inches. What is the width of the box?

10.  Polynomial equations may also have irrational roots

12.  2x 3 – 9x 2 + 2 = 0  2x 3 – 3x 2 –10x – 4 = 0

13.  DAY 1: p186 #15-26  Day 2: p187 #29-35, 40-44  Page186-188 #15-22, 24-35, 40-43  Accelerated: ADD #44-47