Dave4Math / Courses / Polynomial and Rational Functions

Polynomial and Rational Functions

Master polynomial and rational functions. Learn linear, quadratic, polynomials of higher degree, rational functions, and complex numbers. In this course, you'll learn all the basics about polynomials, and you'll get valuable experience working with rational functions.


January 11, 2021

Created by Dave

This course begins Summer 2021.
Current Status
Not Enrolled
Get Started

Are you ready for the best math course in your life? Are you tired of being frustrated and ready to be inspirited? Introducing Dave’s online math course: Polynomial and Rational Functions. Don’t just learn math, be inspired and get confident.

Who This Course is For

  • Students in college who want to learn more mathematics.
  • Anyone interested in polynomial and rational functions.
  • Students who are enrolled in precalculus and want to improve their grade.
  • Anyone interested in getting prepared for calculus 1.
  • Anyone wanting to learn about quadratic functions, polynomial functions, the fundamental theorem of algebra, and rational functions and their asymptotes.


There is no required textbook, though you will need an up-to-date web browser, paper, and pen. A hand-held scientific calculator of your choice is required.

What You’ll Learn in Polynomial and Rational Functions

  • The Graph of a Quadratic Function
  • The Standard Form of a Quadratic Function
  • Finding Minimum and Maximum Values
  • Graphs of Polynomial Functions
  • The Leading Coefficient Test
  • Zeros of Polynomial Functions
  • The Intermediate Value Theorem
  • Long Division of Polynomials
  • Synthetic Division
  • The Remainder and Factor Theorems
  • The Rational Zero Test
  • Other Tests for Zeros of Polynomials
  • The Fundamental Theorem of Algebra
  • Conjugate Pairs
  • Factoring a Polynomial
  • Introduction to Rational Functions
  • Horizontal and Vertical Asymptotes
  • Applications
  • The Graph of a Rational Function
  • Slant Asymptotes
  • More Applications

Course Description

I recommend the prerequisite course Exponentials and Logarithmic Functions. If you’re not sure if this course is for you, checkout the course contents below or find out more by checking out my free precalculus articles.

Course Content

Expand All

David A. Smith

Mathematics Educator

I sincerely believe that the potential in every student can be unlocked. As an accomplished and dedicated instructor, I have firm confidence that I can provide significant value to your studies.

I relish teaching and use it as a channel for my creativity as I seek to deliver real-life and relevant connections between the mathematics that I teach and my students. Promoting an active learning environment and excitement about mathematics is my dream come true.

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.