Factoring is a process that un-multiplies/FOILs/distributes or breaks numbers down. It is used to help simplify the expression so it is easier to work with. When factoring, you’re trying to make the expression that is currently composite, something that can be evenly divide by numbers other than one and itself (ex. 24, 16, 30), to become prime, something that can only be divided by one and itself (ex. 5, 23, 11). Sometimes factoring is simple and you’ll only need to find the factors of single numbers, but this will be about harder types of factoring with polynomials and quadratic equations. This essay will explain several different types of factoring.

The first step in factoring is always finding the GCF or the greatest common factor. That is the largest number that can divide evenly into two or more numbers. Let’s use the example of -14by² - 7b²y + 21by². First we must look for the common factor of the coefficient. The GCF for -14, -7, and 21 is 7. Then there are the variables b and y. In -7b²y there is a b², yet the GCF would be b because the other two terms only have one b. You must take the factor that can go into all the terms. This also applies with the y, so the final GCF for the entire thing would be -7by. Once the GCF is taken out (divided out) it would look like this: 7by(-2y² - b + 3y). This is not the correct answer though. The GCF has to be -7by. Why it wouldn’t it be 7by? When it is factored out you always want to make sure the leading coefficient is positive. When we use 7, the leading coefficient is negative. Change the GCF and correct answer is –7by(2y² + b - 3y).

To factor expressions that don’t have all terms sharing a GCF, you’ll need to do ‘grouping’. When all the terms don’t have a GCF, you need to group two terms together that do have a common factor. Also, an expression with four terms is usually a sign that you will need to use grouping. As an example we can use xy + 5x + y + 5. There are several ways this can be grouped, but let’s...