1. 6.9 Rational Zero Theorem Parts of a polynomial function f(x) oFactors of the leading coefficient = q oFactors of the constant = p oPossible rational roots =

2. Ex 1: List all the possible rational zeros for the given function a. f(x) = 2x 3 – 11x 2 + 12x + 9b. f(x) = x 3 - 9x 2 – x +105

3. Finding Zeros of a function Use Descartes’ rule to find the number of possible zeros of each type Find all the possible rational zeros then use synthetic division to find a number that gives you a remainder of 0 Then factor and or use the quadratic formula with the remaining polynomial to find any other possible zeros –If the degree is 4 or higher- continue synthethic division until you have only x 2 …. remaining then do quadratic formula –If the degree is 3- do quadratic formula right away after finding the first zero

4. Find all the zeros of the given function f(x) = 2x 4 - 5x 3 + 20x 2 - 45x + 18

5. Ex 2: Find all the zeros of the given function f(x) = 9x 4 + 5x 2 - 4

6. Graphing Polynomials a. Rational Zero Theorem : find all zeros b: Make a table with the integers between the zeros c. plot all zeros and table ordered pairs d. Identify any relative minima or maxima