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2.6 Theorems About Roots of Polynomials PG 98
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Objectives Use the Rational Root Theorem to list all possible roots of a polynomial Test possible roots to find actual roots Use Conjugate Root Theorem to find pairs of roots
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Rational Root Theorem
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If a problem asks for “all possible rational roots” then you list all the p/q’s If a problem asks for “rational roots” then: 1.Use your graphing calculator to find 1 root (x= some number like 3). 2.Use that root for synthetic division (plug 3 into the box) to break down the function. 3.Repeat steps 1 and 2 if still have a cubic or higher degree polynomial, until get down to a quadratic polynomial. 4.Now factor or use the quadratic formula to break down to find all the factors and remaining roots.
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Rational Root Theorem
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p. 99 Got It? and Practice 1,2
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Rational Root Theorem
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Conjugate Root Theorem
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p. 100 Got It? and Practice 5,6
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Problem 4 Got it: Pg 101 Replace with the below example
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HW 2.6 Pg 103-105 # 11-15, 17a, 17b, 19, 20, 24, 25
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