Algebra I: 1,001 Practice Problems For Dummies

Chapter 9

Factoring Basics

Factoring algebraic expressions is one of the most important techniques you'll practice. Not much else can be done in terms of solving equations, graphing functions and conics, and working on applications if you can't pull out a common factor and simplify an expression. Factoring changes an expression of two or more terms into one big product, which is really just one term. Having everything multiplied together allows for finding common factors in two or more expressions and reducing fractions. It also allows for the application of the multiplication property of zero. Factoring is crucial, essential, and basic to algebra.

The Problems You'll Work On

In this chapter, you work through factoring basics in the following ways:

• Determining what divides a number by using the rules of divisibility
• Creating prime factorizations of numbers
• Finding a numerical GCF (greatest common factor)
• Factoring out a GCF containing numbers and variables
• Reducing fractions with monomial divisors
• Reducing fractions with polynomial divisors

What to Watch Out For

Here are a few things to keep in mind as you factor your way through this chapter:

• Making sure you apply divisibility rules correctly
• Writing a prime factorization with the correct exponents on the prime factors
• Checking that the terms remaining after dividing out a GCF don't still have a common factor
• Reducing only factors, not terms
• Writing fractional answers with correct grouping symbols to distinguish remaining ...