Chapter 8 Notes

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Rational Root Theorem• A polynomial equation with integral coefficients has the rootwhere h and k are relatively prime integers. Then h must bea factor of the constant term and k must be a factor of thecoefficient of the highest degree term.hk
Steps for the homework• Use Descartes’ Rule of signs to find the number and typesof possible roots. In problems 22-25, first multiply to getrid of the fractions.• Use the Rational Root Theorem to determine all of thepossible rational roots.• Use synthetic division to identify the rational roots of theequation, if any. If you find one rational root then youmust do the next step. If you don’t find one rational rootthen you may stop and your answer will be “no rationalroots”.• Use factoring or the quadratic formula to find theremaining roots.
Page 1 and 2: Section 8-1Direct Variation and Pro
Page 3 and 4: Direct Variation• A linear functi
Page 5 and 6: Section 8-2Inverse and Joint Variat
Page 7 and 8: Inverse Variation• a function def
Page 9 and 10: Example Homework Problem• Suppose
Page 11 and 12: Objectives• to perform polynomial
Page 13 and 14: Steps to perform polynomial long di
Page 15 and 16: Example of polynomial long division
Page 17 and 18: Section 8-4Synthetic Division
Page 19 and 20: Synthetic Division• Synthetic div
Page 21 and 22: Example of synthetic division2x32
Page 23 and 24: Objectives• to use synthetic subs
Page 25 and 26: Steps for homework problems• Prob
Page 27 and 28: Example for Problems 1-8P(x) = x 3
Page 29 and 30: Example for Problems 17-20x 3 + 3x
Page 31 and 32: Example for Problems 29-32x 4 -3x 3
Page 33 and 34: Example for Problems 35-37P(x) = x
Page 35 and 36: Objectives• to write a polynomial
Page 37 and 38: Steps for Homework Problems• Prob
Page 39 and 40: Example for Problems 5-8x 3 -3x 2 +
Page 41 and 42: Example for Problems 13-20• x 4 +
Page 43 and 44: Example for Problems 23 & 24x 3 + 2
Page 45: Objectives• to find the rational
Page 49 and 50: • 2x 2 - 4x + 4 = 0: has a GCF of
Page 51 and 52: Objectives• to approximate to the
Page 53 and 54: Steps for homework• Perform Desca
Page 55 and 56: 1 1 -3 0 0 51 -2 -2 -21 -2 -2 -2 32
Page 57 and 58: Objectives• to approximate values
Page 59: Example Homework Problem• Approxi

Chapter 8 Notes

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