This week in Pre-calc 11, we started our factoring review from grade 10. I want to focus on factoring polynomials; something new I learned is a simple way you can factor polynomials easily because they look very complicated when you first look at them and are told to factor them this method is called “Factoring by Grouping”.

Factoring by grouping simply is an area method you draw a square and divide it into 4 sections to fill in the numbers you have to figure out the factored answer for.

Example #1

Let’s start with this example, here what you have to do is draw your area square and fill in the terms each in a section. x^2 should always be found in the top left box, and the constant which is the number with no variables is always in the bottom right box, and the other two terms (like terms) would be diagonal. After filling out the box you need to find the GCF (Greatest Common factor) for all the terms. In the photo, I showed you what it looked like for the first 2 terms (first row across). So, you look at the first row x^2 and 2x the GCF here is x so write it outside the box, then look at the second row 6x and 12 the GCF is 6, continue doing the same thing for both columns and by grouping both terms that are on top the box in brackets and the terms on the side then you get a binomial; you should get what I’ve highlighted in green and that will be the factored answer (x+6)(x+2). To verify if the binomial you’ve ended up with is correct you can do foil and if it was correct you should get back to the original equations you’ve begun with.

Example #2

Here let’s try a similar example just adding a negative to the terms of the polynomial. Draw the area box method fill in the terms keep like terms diagonal from each other, and figure out the GCF remember that there are negative numbers, you will know if you have to make both terms negative or only one. In this example, I know that both have to be negative to give me a positive constant (45), but if it was -45 you simply know only one term has to be negative. After you have all four terms outside the box you now can group both expressions to end with a binomial. Always verify you’re results by foiling. For me, I don’t have to foil because as I’m figuring out the GCF I check if it works for other terms, there are many ways, figure out your way and math will be easier. It’s mostly about observing and what you notice.

Example #3

Here we follow all the previous steps we talked about, but what’s different here is that the bottom row contains a -a and a 3, what do you do in this situation? Well, there is no GCF simply it’s a 1 because 1 is divisible by everything, and because we have a -a and we have to end up with a positive 3 constant the GCF is going to be -1. Then Group both expressions and if you want to verify go ahead and foil.

Things to remember:

• The squared variable is always in the top left box.
• Like terms (like variables) are always diagonal from each other.
• The constant is always in the bottom right box.
• Sometimes you might wonder if you have things in the wrong place well here’s a brilliant trick for you. Multiply the 2 terms diagonally and the two products should be the same as shown in the photo provided. If the two products didn’t equal you might have to rearrange your terms.