How to Factor a Polynomial With 5 Terms

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How to Factor a Polynomial With Large Exponents....5

Factoring a polynomial with five terms isn't necessarily more difficult than factoring another type of polynomial - it just might be more time consuming. Factor a polynomial with five terms 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 show you how to factor a polynomial with five terms. So let's start with a polynomial with five terms, 14X to the seventh power plus 10X to the fourth power minus 12X squared plus 6X minus 4. Okay, so one, two, three, four, five terms in this polynomial. You're more than likely going to factor a polynomial with five terms by using just greatest common factor so what we're going to do is first look at the numerical values and we're going to see if they have anything in common that we can pull out. So we have 14, 10, 12 and 4 and the greatest common factor of all of those numbers is going to be 2. So that means that we're able to pull a 2 out of this polynomial. And now we're going to look at the variables. We have X squared, X to the fourth, X squared, I'm sorry, X to the seventh, X to the fourth, X squared, X and then my last term doesn't have a variable so while it looked like there was going to be a common factor with X, there isn't because each term has to have that common factor in order for me to pull it out so that means that I cannot take an X out of this. I'm going to have to just factor out a 2. So when I factor out this 2, I just divide the entire polynomial by my GCF and when I divide 14X to the seventh by 2, I'm going to get 7X to the seventh plus 5X to the fourth minus 6X squared plus 3X minus 2 and these are the two factors that are going to get me back to this polynomial. After you've factored it, you should always check inside to see if you can further factor the polynomial you've created and in this case I can't so I would be done. My name is Marija, and I just showed you how to factor a five term polynomial.

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