What Is a Non-Factorable Polynomial?

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A non-factorable polynomial is also known as a prime polynomial. Learn about a non-factorable polynomial with help from an experienced educator in this free video clip.

Part of the Video Series: Lessons in Math
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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to tell you what a non-factorable polynomial is. So, a non-factorable polynomial is also known as a prime polynomial. A simple example would be something like, X plus five. So, if I tried to factor X plus five, I'm thinking of all of the different ways I can factor, and it's not a quadratic, so I can't try to use the quadratic equation or product and sum. It's not a difference of squares. Nothing pops out of me. And GCF is always the simplest way to try to factor. So, when I look for the GCF of the two terms in this polynomial, the only factor of both X and five is the number one, and you never factor out the number one, because you end up with the same exact expression you started with, just multiplied by one. So, this would be a non-factorable polynomial, a simple version. So, a more complex non-factorable polynomial would be, for example, four, let's say, X squared plus, let's see, X--or, actually, I guess we can make that cubed--plus nine. So, again, there's no greatest common factor of any of the three terms, therefore, I can't factor anything out, and this is called a prime polynomial. It is non-factorable. My name is Marija, and I just showed you what a non-factorable polynomial is.

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