Algebra I: 1,001 Practice Problems For Dummies

Chapter 8

Dividing Algebraic Expressions

Division is the opposite or inverse of multiplication. Instead of adding exponents, you subtract the exponents of like variables. When dividing an expression containing several terms by an expression containing just one term, you have two possible situations: the divisor evenly divides each term, meaning fractions formed from each term and the divisor reduce to denominators of 1, or the divisor doesn't evenly divide one or more of the terms. What you do with the second situation depends on the application you're working on at the time. The problems in this chapter present various options.

The Problems You'll Work On

The problems in this chapter are all about division and include the following:

• Dividing several terms by a number
• Dividing several terms by a term containing numerical and variable factors
• Dividing several terms by a binomial, using long division
• Dividing several terms by a binomial, using synthetic division
• Dividing by trinomials

What to Watch Out For

As you work through dividing one expression after another, watch out for the following:

• Assigning the correct sign to each term in the result
• Remembering to change the sign of each term when dividing by a negative term
• Changing the signs of all products of quotient term times divisor term in each step of a long division problem
• Inserting zeros for missing terms when using synthetic division
• Changing the sign of the number in the binomial when setting up a synthetic division ...