# Types of Factorization

Group #1: Greatest Common Factor

Then the common factors are those that are found in both lists: It is simply the largest of the common factors. In our previous example, the largest of the common factors is 15, so the Greatest Common Factor of 15, 30 and 105 is 15 The "Greatest Common Factor" is the largest of the common factors ...

Group #2: Grouping

Factorization by grouping means that we need to group the terms with common factors before factoring. Method of factorization by grouping the terms: (i) From the groups of the given

Group #3: Difference in Two Squares

A Difference Between Two Squares is an expression with two terms (also known as a binomial) in which both terms are perfect squares and one of the two terms is negative. The problems that follow show how to factor a difference between two squares.

source: wyzant.com
Group #4

Create smaller groups within the problem, usually done by grouping the first two terms together and the last two terms together. Step 3: Factor out the GCF from each of the two groups. In the second group, you have a choice of factoring out a positive or negative number.

source: mesacc.edu
Group #5: Trinomials

Write down all factor pairs of 4 (Note: since 5 is positive we only need to think about pairs that are either both positive or both negative. Remember a negative times a negative is a positive. As the chart on the right shows you -2*-2 is positive 4...so we do have to consider these two negative factors.

Group #6: General Trinomials

Formula For Factoring Trinomials (when a =1) It's always easier to understand a new concept by looking at a specific example so you might want to do that first. This formula works when 'a' is 1. In other words, we will use this approach whenever the coefficient in from of x 2 is 1. (If you need help factoring trinomials when \$\$a \ne 1 \$\$, then go here.