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Math: Factoring by Grouping - Tutorial
Finding the Greatest Common Factor
You can say that 1, 2, 3, 4, 6, and 12 are all factors of the number 12.
You can use factoring to simplify expressions and to solve equations.
Let's begin by finding the greatest common factor of the expression 5x + 15.
You may recall that expressions are made up of terms. This expression
has 2 terms: 5x and 15
Example 1:
If you wanted to find the factor of the expression 5x + 15, you would look for the
largest number that is a factor of both 5x and 15. To do this, look at each term separately.
When an expression has four or more terms, the expression can be simplified using factoring by grouping. Here are three rules to follow.
1. Separate terms into pairs that have common factors.
2. Factor out the common factor.
3. Put the common factor in front of the remaining factors.
FOIL Multiplication and Factoring
Trinomials
Trinomials are expressions with three terms. You can use a method called
FOIL to help you simplify. The letters of FOIL stand for:
F - multiply the two first terms
O - multiply the two outer terms
I - multiply the two inner terms
L - multiply the two last terms
Let's multiply (x + 2) by (x + 4) the long way.
This section will cover the fundamentals and rules of factoring by grouping.
Example 2:
By looking at the factors for each term, you see that 3, a, and b are the greatest common factors.
You can factor this expression by writing:
If you multiply 3ab times teh terms inside of the parentheses, you will get the original expression.
Factoring by Grouping
Factors are the numbers needed to arrive at a product in a multiplication problem or algebraic expression.
Example: There are three ways to multiply to get the number 12:
