How to Factor a Polynomial With Large Exponents

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Just because a polynomial has large exponents doesn't make it any more difficult to factor. Factor a polynomial with large exponents 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 polynomials with large exponents. So let's say for example we have 15X to the 20th power minus 20X to the 18th power. So the exponents are fairly large but that doesn't mean that it makes my problem harder at all. All I have to do is look for the GCF of these two terms. So numerically the GCF is going to be 5, right 5 is the greatest common factor of 15 and 20 and then if I look at the variables, I have X to the 20th power and I have X to the 18th power. That means that the largest amount of Xs that I could allow would be X to the 18th power. So once I've removed the GCF I'm going to go ahead and open a parentheses, divide the polynomial by the GCF to get the other factor. So 15X to the 20th power divided by 5X to the 18th power is going to give me 3X squared minus 20X to the 18th power divided by 5X to the 18th power is going to just give me 4. So now I have 5X to the 18th power multiplied by 3X squared minus 4 and I've just factored a polynomial with fairly large exponents and you don't always have to factor by GCF and sometimes it might lead to further factoring. So for example if you have X to the 14th power minus X to the 12th power the highest polynomial that I could pull out or monomial is X to the 12th power and when I do that I end up with X squared on the inside minus 1. But now I realize that inside I can use difference of squares because X squared minus 1 is the same as X plus 1, X minus 1, so this factors a little further into X to the 12th multiplied by X plus 1 times the quantity of X minus 1. And that's the complete factorization of this polynomial here. My name is Marija, and I just showed you how to factor polynomials with large exponents.

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