Factoring

Factoring is the process of finding the factors of a number. The factors of a number are the numbers that divide evenly into the number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

To factor an algebraic expression, we need to find the factors of the expressions. For example, to factor the expression x^2+5x+6, we need to find the factors of 6 that add up to 5. The factors of 6 are 1, 2, 3, and 6. The only two factors of 6 that add up to 5 are 2 and 3. So, the factored form of x^2+5x+6 is (x+2)(x+3).

There are a few different types of factoring that we can use to factor algebraic expressions. One type of factoring is called greatest common factor factoring. This is when we factor out the greatest common factor from an expression. For example, the greatest common factor of 18 and 24 is 6. So, we can factor out a 6 from each term to get 6(x+3) and 6(x+4).

Another type of factoring is called difference of squares factoring. This is when we have an expression that is the difference of two squares. For example, x^2-9 is the difference of two squares. We can factor this expression as (x+3)(x-3).

A third type of factoring is called perfect square trinomials. This is when we have an expression that is the square of a binomial. For example, (x+5)^2 is a perfect square trinomial. We can factor this expression as (x+5)(x+5).

There are also a few special cases that we need to be aware of when factoring. One special case is when we have an expression that is the difference of two cubes. For example, x^3-27 is the difference of two cubes. We can factor this expression as (x-3)(x^2+3x+9).

Another special case is when we have an expression that is the sum or difference of two cubes. For example, x^3+27 is the sum of two cubes. We can factor this expression as (x+3)(x^2-3x+9).

The last special case is when we have an expression that is the product of two binomials. For example, (x+5)(x-5) is the product of two binomials. We can factor this expression as (x+5)(x-5).

Factoring is a great tool to use when solving equations and graphing linear equations. By factoring an expression, we can simplify it and sometimes even solve it.