Subject:
Mathematics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Mathematics, Tmm0022
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Text/HTML

Polynomials - Introduction, Zeros and Their Multiplicities, End-Behavior, Graphing

Section 1: Polynomials - Part 1

Providing a motivation to study polynomials will go a long way. A brief review of factoring binomials and trinomials can be done concurrently with the problem of solving for x-intercepts. The topic on sign chart to determine the behavior of a polynomial around its zeros can be used concurrently with the topic of solving polynomial inequalities.

Designer curves used in automotive and roller coaster rides, functions modeling human physiology, models analyzing a business's performance, for example, have polynomials in common. A polynomial is a linear combination of basic power functions xk. Linear and quadratic functions are special polynomials. In this module you will learn about graphing a polynomial by studying its end-behavior and the multiplicities of its zeros.

Review:

  • Linear and quadratic equations and be able to solve them with ease
  • Factoring binomials and quadratic expressions

Learning Objectives: By the end of this module you should be able to

  • determine domain and range of a polynomial
  • identify the degree, leading term, leading coefficient and constant term of a polynomial
  • use the graphs of basic power functions to anticipate the graph of a polynomial
  • use factoring to find the zeros or x-intercepts of a polynomial
  • find y-intercept
  • study the end-behavior of a polynomial
  • understand and apply Intermediate Value Theorem to a polynomial
  • make a sign chart for a polynomial using its zeros and their multiplicities
  • sketch the graph of a polynomial without a graphing calculator
  • identify intervals of increase and decrease for a polynomial