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
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 6.6
- This is an extremely important section. It covers solving algebraically by factoring as well as solving graphically by finding the roots of the equation. This material will be used throughout the remainder of the course so be sure to get it down pat! There are also some important application problems to study. (Yeah, word problems!)
- example 7 Read through the modeling motion example but pay particular attention to the use of the zero product rule to solve the equation. We will discuss the height function further much later in the course.
- example 8 This and similar geometry applications are important to be able to work. Fair game for the quiz!