Chapter 8 Notes

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Remainder and Factor Theorems• Remainder Theorem: Let P(x) be a polynomial of positivedegree n. Then for any number c, P(x) = Q(x) • (x - c) + P(c)where Q(x) is a polynomial with degree n - 1.• Factor Theorem: The polynomial P(x) has x - r as a factor ifand only if r is a root of the equation P(x) = 0.
Steps for homework problems• Problems 1-8: perform synthetic division using the valueof c.• Problems 9-16: perform synthetic division with the valuethat makes the binomial zero. If the remainder is zeroanswer “yes”, if the remainder isn’t zero answer “no”.• Problems 17-20: perform synthetic division with the givenvalue and then factor or use the quadratic formula to breakdown the quotient polynomial.• Problems 21-28: write each number a s a factor and thenmultiply the binomials together.• Problems 29-32: perform synthetic division with the firstvalue given, then perform synthetic division on thequotient with the second value given. Either factor or usethe quadratic formula on the final quotient to find lastroots.
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: Objectives• to use synthetic subs
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 and 46: Objectives• to find the rational
Page 47 and 48: Steps for the homework• Use Desca
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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