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Chapter 9

Chapter 9. Polynomials and Rational Functions. In this chapter, you will …. Learn to write and graph polynomial functions and to solve polynomial equations. Learn to use important theorems about the number of solutions to polynomial equations.

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Chapter 9

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  1. Chapter 9 Polynomials and Rational Functions

  2. In this chapter, you will … • Learn to write and graph polynomial functions and to solve polynomial equations. • Learn to use important theorems about the number of solutions to polynomial equations. • Learn to solve problems involving permutations, combinations and binomial probability.

  3. Polynomial and Rational Models Section 9.1

  4. A monomial is an expression that is a real number, a variable or a product of real numbers and variables.13,    3x,  -57, x²,   4y²,  -2xy,  or  520x²y² A binomial is the sum of two monomials.  It has two unlike terms.  3x + 1,   x² - 4x,     2x + y,    or    y - y² A trinomial is the sum of three monomials.  It has three unlike terms. x2+ 2x + 1,   3x² - 4x + 10,      2x + 3y + 2 A polynomial is the sum of one or more terms.  x2+ 2x,  3x3+ x² + 5x + 6, 4x - 6y + 8

  5. The exponent of the variable in a term determines the degree of that term. • The terms in the polynomial are in descending order by degree. • This order demonstrates the standard form of a polynomial. 2 3 2x -5x -2x + 5 Leading Coefficient Cubic Term Quadratic Term Linear Term Constant Term

  6. Example 1 Classifying Polynomials Write each in standard form and classify it by degree and number of terms. • -7x + 5x4 • x2 – 4x + 3x3 +2x • 4x – 6x + 5

  7. Assignment • Class Work Page 509-510 [#s 2-5; 12-15; 17-25] ~ See page 657 for Formulas to use on questions 2-5 • Home Work: Worksheet 9.1 Due Tuesday.

  8. Power and Quotient Rules Section 9.2

  9. Properties of Exponentsa&b are real numbers, m&n are integers • Product Property: am * an=am+n • Power of a Power Property: (am)n=amn • Power of a Product Property: (ab)m=ambm • Negative Exponent Property: a-m= ; a≠0 • Zero Exponent Property: a0=1; a≠0 • Quotient of Powers: am= am-n;a≠0 an • Power of Quotient: b≠0

  10. Example 1 – Product Property • (-5)4 * (-5)5 = • (-5)4+5 = • (-5)9 = • -1953125

  11. Example 2 • x5 * x2 = • x5+2 = • x7

  12. Example 3 – Power of a Power • (23)4 = • 23*4 = • 212 = • 4096

  13. Example 4 • (34)2 = • 34*2 = • 38 = • 6561

  14. Example 5 – Neg. Exponent • (-5)-6(-5)4 = • (-5)-6+4 = • (-5)-2 =

  15. Example 6 – Quotient of Powers

  16. Example 7 – Power of Quotient

  17. Example 8 – Zero Exponent • (7b-3)2 b5 b = • 72 b-3*2 b5 b = • 49 b-6+5+1 = • 49b0 = • 49

  18. Example 9 – Quotient of Powers

  19. You Try

  20. Answers

  21. Assignments • Class Work Page 517 [#s 2-19; 21-29; 32- 46] • Homework: Worksheet 9.2 ALL Due Thursday

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