Topic: Factoring

Subtopic: Polynomial Equations

**Overview**

A polynomial equation (e.g., x^3-2x^2-3x=0) can be solved by factoring and using the zero-product rule (e.g., x(x+1)(x-3)=0 gives x=0,-1,3). Knowing how to accurately factor down completely is key! Watch for GCFs and special factoring forms.

**Objectives**

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

- 7.4.1 Differentiate between "factoring a polynomial expression" and "solving a polynomial equation".
- 7.4.2 Solve polynomial equation by factoring and using the zero-product rule (This is key!)
- 7.4.3 Recognize how many solutions a polynomial equation will have by observation of its factored form
- 7.4.4 Recognize how many zeros a polynomial function has by observation of its graph
- 7.4.5 Electronically graph a polynomial function and find its x-intercept values
- 7.4.6 Know that the x-intercept values on the graph of a polynomial function f(x) are the solutions to the equation f(x)=0
- 7.4.7 Write solutions as a list (e.g., x=0,-1,3) or as a solution set (e.g., {0,-1,3})

**Terminology**

Define: quadratic equation, polynomial equation, zero-product rule, x-intercept point, x-intercept value, zero of a function

**Supplemental Resources**

Read my Lecture - Applications of Factoring Polynomials for motivation.

It is recommended that you be able to use a calculator (handheld or software) to solve a polynomial equation graphically by electronically finding its x-intercept values. If you have a handheld graphing calculator then these sites may help:

- For TI-84 (TI=Texas Instruments) see:

Prof. Milner's Graphing Calculator Tutorial Videos: Find the root or zero of an equation

- For TI-86 or TI-89 see:

Prof. Keely's Calculator Guide: x-Intercept Points

- For other models (or makes) try searching on one of the sites recommended here: FAQs - Graphing Calculator Tutorials