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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.

  1. Factoring Numbers -- Start Here
  2. Finding a Greatest Common Factor
  3. Factoring a GCF from an expression
  4. Factoring a Difference Between Two Squares
  5. Factoring Trinomials
  6. Factoring Completely
  7. Solving Equations by Factoring
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