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.

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Presentation transcript:

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 =

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

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

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

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

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