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


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`.


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


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

STUDY: Polynomial Functions and Graphs - Introduction, Real Zeros, Synthetic Division, Remainder Theorem, Factor Theorem

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