Sometimes factoring a polynomial doesn’t fit into an easy to define mold or formula, and we need to use an alternative method to factor a polynomial completely: Factoring by grouping.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
We will start off by factoring trinomials by grouping, to understand the process and steps, and then expand our knowledge to factor polynomials by grouping.
The second type of factoring by grouping that we are going to look at is when we have a polynomial of four terms.
At first glance, these types of polynomials will not look factorable, but if we follow the steps for factoring by grouping, which means to group the first two terms together and the last two terms together, we will quickly see that within these groups there is a GCF that can be pulled out.
Factoring by Grouping Example
By placing the original polynomial in groups, as Khan Academy accurately states, we were able to identify the greatest common factor, which turns out to be a binomial!
Cool!
Now I think it’s important to note that some students will quickly recognize that all we are doing is just factoring out a binomial, while others will think of factoring by grouping as factoring the GCF twice.
For example, with 2n^3 – n^2 -10n +5, some students will notice that we need to factor out (2n-1) while others will need to factor out the gcf from the first two terms and the gcf from the last two terms separately in order to create the binomial of (2n-1). But the great thing is that whichever way you “see” it, you will arrive at the same answer of (2n-1)(n^2-5).
So, regardless of whether you see the binomial right away or prefer to factor out one term at a time, this video is right for your. Additionally, you will notice in this video you will hear me say, “factor our the binomial” or let’s “factor two times,” to encourage everyone, regardless of their preferred method, as we learn this new skill.
Also, please note that depending on your teacher or textbook, the amount of simplification will vary. For example, both of the following answers would be considered correct.
[(x-2)(x+2)+4y][(x-2)(x+2)-4y] or ( x^2 – 4 + 4y)( x^2 – 4 – 4y)
And lastly, we will look at for factoring polynomials completely is one where we will need more than one method of factoring. For these types of polynomials, we will use the technique of factoring by grouping, but also employ our knowledge of the difference of squares.
Factor by Grouping (How-To) – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.