How Do I Know What Type of Factoring I Should Do?
Do you have a problem to factor, and you don’t know where to start? Follow this list! This list is an overview of the most common types of factoring you will see in high school or college math; it works best if you already have an understanding of what factoring is and have already been exposed to multiple examples. Good luck to you and study hard!
Start by determining how many terms you have in your expression
2 terms:
a) Determine if there is a greatest common factor (GCF) of your 2 terms and factor it out. This might be all that is possible for your problem OR you might be able to continue and do methods b or c.
https://www.youtube.com/watch?v=iTn3TTF0IXk
b) See if you have a difference of squares. BOTH terms have to be squares and there needs to be a subtraction sign.
https://www.youtube.com/watch?v=HLNSouzygw0
c) If you have 2 terms but you do not have a difference of squares or GCF, see if you have a sum or difference of cubes.
https://www.youtube.com/watch?v=CxcP4ylUP5w
3 Terms:
a) If your expression has 3 terms (called a trinomial), make sure it is in standard form and the exponents are written in descending order :
4x3 + 6x2 + 11x
https://www.youtube.com/watch?v=K8Mish9aORU
This might be all you can do. Look at what’s left inside the parenthesis and go through this list again to see if your expression matches any cases to factor further.
ax²+bx+c
Determine your a,b and c values
https://www.youtube.com/watch?v=BlTcuLNzM3c&t=323s
b) If your “a” value is not 1, see if there is a GCF between all 3 of your terms. If there is, factor it out and rewrite your expression. If there is no GCF, continue to method c. After you factor out the GCF, look at your new a,b,c values. If your “a” value is now 1, you can do the method in Step a. Don’t forget to keep your GCF in your final answer!
Here’s another video for reference. This particular example starts at 3:05
https://www.youtube.com/watch?v=U6FndtdgpcA
c) If your “a” value is not 1, do this method
Box Method: https://www.youtube.com/watch?v=szGj9C0Djaw
https://www.youtube.com/watch?v=OKkg2kUsDq4
https://www.youtube.com/watch?v=07g-l8OuGPo
4 Terms:
a) If your expression has 4 terms try to factor by grouping. As always, see if there is a GCF you can pull out of all 4 terms first before you begin this method (don’t forget to keep it in your final answer!)