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: x² + 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 x² + 3x + 2.) Here, (x + 1) and (x + 2) are factors of x² + 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.