Algebra I All-in-One For Dummies

Chapter 10

Dividing the Long Way to Simplify Algebraic Expressions

IN THIS CHAPTER

Dividing one or more terms by a single term

Working with binomial and trinomial divisors

Simplifying the process with synthetic division

Using long division to simplify algebraic expressions with variables and constants has many similarities to performing long division with just numbers. The variables do add an interesting twist (besides making everything look like alphabet soup) — with the exponents and different letters to consider. But the division problem is still made up of a divisor, dividend, and quotient (what divides in, what’s divided into, and the answer). And one difference between traditional long division and algebraic division is that, in algebra, you usually write the remainders as algebraic fractions.

Dividing by a Monomial

Dividing an expression by a monomial (one term) can go one of two ways.

• Every term in the expression is evenly divisible by the divisor.
• One or more terms in the expression don’t divide evenly.

If a fraction divides evenly — if every term can be divided by the divisor — then the denominator and numerator have a common factor. For instance, in the first example ...