# Introduction To Factoring

A composite number is a number that can be written as the product of two
positive integers other than 1 and the number itself. For example: 14 is a
composite number because it can be written as 7 times 2. In this case, 7 and 2
are called factors of 14.

A composite expression is similar in that it can be written as the product of
two or more expressions. For example: x^{2} + 3x + 2 is
composite because it can be written as (x + 1)(x + 2). (Recall that the
FOIL Method shows that
(x + 1)(x + 2) is equivalent to x^{2} + 3x + 2.) Here, (x + 1) and
(x + 2) are factors of x^{2} + 3x + 2.

In general, a number is a factor of another number if the first number can
divide the second without a remainder. Similarly, an expression is a factor
of another expression if the first can divide the second without a remainder.

#### Definition

A **prime number** is a number greater than 1 which has only two positive
factors: 1 and itself. For example, 11 is a prime number because its only
positive factors are 1 and 11.
Factoring is a process by which a the factors of a composite number or a
composite expression are determined, and the number or expression is written
as a product of these factors. For example, the number 15 can be
factored into: 1 * 15, 3 * 5, -1 * -15, or -3 * -5.
The numbers -15, -5, -3, -1, 1, 3, 5, and 15 are all factors of 15 because they
divide 15 without a remainder.

Factoring is an important process in algebra which is used to
simplify expressions, simplify fractions, and solve equations.
The next few lessons explain how to factor numbers, expressions, and equations.

**Factoring Numbers -- Start Here**
- Finding a Greatest Common Factor
- Factoring a GCF from an expression
- Factoring a Difference Between Two Squares
- Factoring Trinomials
- Factoring Completely
- Solving Equations by Factoring