Differences Between Dividing & Factoring

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Dividing and factoring are two completely different concepts and should be treated as such. Learn about differences between dividing and factoring with help from an experienced mathematics educator in this free video clip.

Part of the Video Series: Elementary Math
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Video Transcript

Hi my name is Marija. I'm a mathematician and today I'm going to tell you the differences between dividing and factoring. Now factoring includes dividing, that's one of the steps but in addition to that you have to find the greatest common factor. So we're going to take an expression like 2X to the 4th power minus 10X cubed plus 20X squared. If I wanted to factor this expression, what I have to do first is find the GCF. So the greatest common factor of these three terms is going to be, numerically it's going to be 2 and when we're dealing with the variables it's going to be X squared. So the first step to factoring is to find the GCF. If you are doing it in that method. So 2X squared is my GCF. Now we're dividing each of these three terms by 2X squared. So factoring includes division but it's only the second step to it. So I'm going to do 2X to the fourth power divided by 2X squared and I get X squared. I'm going to do negative 10X cubed divided by 2X squared. I'm going to get negative 5X and I'm going to get 20X squared divided by 2X squared which gives me positive 10. Okay so now I have factored and I can actually go ahead and factor again inside if I wanted to but in order to factor this initially through GCF I had to find the GCF first and then divide each term by the GCF. So while factoring includes division that's not the only step in it. My name is Marija and I just told you the differences between division and factoring.

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