Course: College Algebra
Topic: Polynomial and Rational Functions
Subtopic: Polynomial Functions III - Complex Zeros, Fundamental Thm of Algebra, Descartes Rule


Completing our study of polynomial functions, in this lesson we turn to complex zeros which will enable us to factor ANY polynomial. The Fundamental Theorem of Algebra shows that the degree of the polynomial matches the number of its roots when factored in the complex realm. Descartes Rule of Signs classifies the possible roots. The Rational Roots Theorem helps us list all the possible roots and synthetic division helps us find the actual roots.


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


Terms you should be able to define: complex zeros, conjugate pairs, Fundamental Theorem of Algebra, Rational Roots Theorem, Descartes, Descartes Rule of Signs, Descartes Root Chart, Upper/Lower Bounds Theorem

Mini-Lectures and Examples

STUDY: Polynomial Functions and Graphs - Complex Zeros, Fundamental Theorem of Algebra, Descartes Rule of Signs

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