3-Polynomials

Important Concepts for This Unit

Functions defined by polynomial expressions are called polynomial functions. The graphs of polynomial functions can have many peaks and valleys; this makes them suitable models for many real-world situations. The standards that will be assessed in this chapter are

3.2 Can graph polynomials using intercepts, end behavior, root multiplicity, and transformations.




 

u3.1 - Quadratic Functions and Models

 

  • Graphing quadratic functions
  • Obtaining the exact coordinates of the vertex by completing the square.
  • Finding roots using the quadratic formula.

 

Core Exercises: 2, 7, 12, 23, 30, 35, 42, 46, 53, 63 

Recommended:
 2, 3, 6, 7, 12, 15, 23, 25, 30, 35, 38, 42, 43, 46, 49, 52, 53, 54, 58, 63, 65, 66


   u3.2 - Polynomial Functions and their Graphs

  • The terminology and notation associated with polynomial functions.
  • Characteristics of polynomial graphs: smoothness, continuity, end behavior, and boundaries on the number of local maxima and minima.
  • Graphing polynomials using the zeros (taking into account multiplicity) and end behavior.

 

Core Exercises: 1, 8, 12, 16, 29, 36, 46, 54, 61, 67, 77, 79, 84, 88

Recommended: 1, 2, 5, 8, 10, 12, 13, 16, 17, 22, 23, 29, 36, 39, 44, 46, 49, 51, 54, 57, 61, 63, 67, 71, 75, 77, 79, 81, 84, 86, 88, 90

 


  u3.3 Dividing Polynomials

  • The division algorithm for polynomials.
  • Synthetic division.
  • The Remainder and Factor Theorems.

 

Core Exercises: 2, 4, 11, 17, 26, 38, 45, 52, 54, 58, 61, 66

Recommended:
 1, 2, 4, 5, 9, 11, 14, 17, 19, 24, 26, 30, 36, 38, 41, 45, 47, 51, 52, 54, 55, 58, 60, 61, 63, 66, 68, 68, 75

 

 


  u3.4 Real Zeros of Polynomials

  • The Rational Zeros Theorem: The rational zeros of a polynomial function are always quotients of factors of the constant and the leading terms.
  • Factoring large polynomials using the Rational Zeros Theorem and the quadratic formula.
  • Bounding the number and size of zeros of a polynomial function.

 

Core Exercises: 2, 6, 14, 17, 25, 30, 39, 58, 55, 66, 70, 79, 85, 88, 91, 102, 106, 110

Recommended: 2, 4, 6, 8, 11, 14, 15, 17, 19, 25, 26, 30, 32, 36, 39, 45, 52, 55, 57, 58, 61, 64, 66, 70, 72, 77, 79, 82, 85, 87, 88, 91, 93, 96, 100, 102, 104, 106, 107, 110

 


  u3.6 Rational Functions

  • Various kinds of asymptotes and end behavior of functions, particularly rational functions.
  • Graphing rational functions.

 

Core Exercises: 3, 4, 10, 13, 22, 29, 32, 37, 47, 60, 65, 76, 79, 89

Recommended: 2, 3, 4, 7, 9, 10, 13, 16, 19, 22, 25, 28, 29, 32, 34, 37, 41, 44, 47, 49, 53, 60, 62, 65, 71, 76, 77, 79, 84, 89, 91


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Nikhil Joshi,
Nov 16, 2016, 9:58 AM
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Nikhil Joshi,
Dec 1, 2016, 11:37 AM