Chapter 2: Polynomial and Rational Functions Summary
Course Textbook by Blitzer, PreCalculus Essentials 4th edition, Pearson
Section 1: Be Able To
 Add and subtract complex numbers
 Multiply complex numbers
 Divide complex numbers
 Perform operations with square roots of negative numbers
 Solve quadratic equations with complex imaginary solutions
 Apply the concepts: Reference page 299 problems 61, 62
Section 2: Be Able To
 Recognize characteristics of parabolas
 Graph parabolas
 Determine a quadratic function’s minimum or maximum value
 Solve problems involving a quadratic function’s minimum or maximum value
 Apply the Addition Property of Equality to solve a linear equation in one variable
 Apply the concepts: Reference pages 314 – 315 problems 57 - 76
Section 3: Be Able To
 Identify polynomial functions
 Recognize characteristics of graphs of polynomial functions
 Identify zeros and their multiplicities
 Use the Intermediate Value Theorem
 Understand the relationship between degree and turning points
 Graph polynomial functions
 Apply the concepts: Reference pages 332 – 333 problems 73 - 76
Section 4: Be Able To
 Use long division to divide polynomials
 Use synthetic division to divide polynomials
 Evaluate a polynomial using the Remainder Theorem
 Use the Factor Theorem to solve a polynomial equation
 Apply the concepts: Reference pages 344 – 345 problems 51 - 66
Section 5: Be Able To
 Use the Rational Zero Theorem to find possible rational zeros
 Find zeros of a polynomial function
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Solve polynomial equations
Use the Linear Factorization Theorem to find polynomials with given zeros
Use Descartes’s Rule of Signs
Apply the concepts: Reference page 358 problems 61 - 64
Section 6: Be Able To
 Find the domains of rational functions
 Use arrow notation
 Identify vertical asymptotes
 Identify horizontal asymptotes
 Use transformation to graph rational functions
 Graph rational functions
 Identify slant asymptotes
 Apply the concepts: Reference pages 378 – 379 problems 99- 108
Section 7: Be Able To
 Solve polynomial inequalities
 Solve rational inequalities
 Apply the concepts: Reference page 392 problems 75, 76
Section 8: Be Able To
 Solve direct variation
 Solve inverse variation
 Solve combined variation problems
 Solve problems involving joint variations
 Apply the concepts: Reference page 402 – 403 problems 21 - 37
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