Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Intermediate Algebra
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

Terms you should be able to 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: