Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Polynomial and Rational Functions
Subtopic: Polynomial Functions I - Introduction, Zeros

Overview

Welcome to the study of polynomial functions and their graphs! The theorems and processes included in this topic will enable us to factor, solve, and graph large polynomials. For each new theorem, practice using just that single process, but keep in mind the big picture. Our eventual goal is to pull all the separate theorems together in one big multi-step problem such as completely algebraically without the aid of a calculator factor and graph a polynomial like f(x) = 4x^5 + 12x^4 - 41x^3 - 99x^2 + 10x + 24.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.2.1 Know the definition of polynomial function and recognize functions that are not polynomial
• 3.2.2 Find the degree of a polynomial function and recognize the leading term
• 3.2.3 Find the y-intercept point of a polynomial function algebraically and graphically
• 3.2.4 Find the x-intercept points of a polynomial function algebraically and graphically
• 3.2.5 Use the leading coefficient test to find the end behavior of a polynomial function
• 3.2.6 Understand the effect of the degree (odd vs. even) of each factor of a polynomial function on the graph of the function
• 3.2.7 Use the Turning Point Theorem to find the maximum number of turning points a polynomial's graph could have

Terminology

Terms you should be able to define: polynomial function, degree, leading term, leading coefficient, zeros, roots, end behaviour, multiplicity, turning points

Mini-Lectures and Examples

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics:
"Determining the Characteristics of Polynomial Functions"
"Finding the Zeros of Polynomial Functions"

rev. 2020-10-10