Dividing Polynomials

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Dividing polynomials requires simplifying the terms of the fraction using multiplication and then completing the division equation. Watch an example of a problem requiring division of polynomials with help from a math teacher in this free video math lesson.

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Video Transcript

So how do you divide polynomials? That's sounds really hard isn't it? Hi, I'm Jimmy, I've been teaching college math for nine years and we're here to tell you how a little few, just little steps on how to divide polynomials. Now, there's a basic structure and as long as you remember the long division steps from previous courses with numbers, then those steps will carry over in to dividing polynomials. There's one little detail that you have to keep in mind but we'll get to that very shortly. Now, here's an example. You have three x squared plus two x plus one dividing by x plus two. Now the first thing that you want to take note of is because you're dividing by two terms, Your answer will begin on top of the second term. Now, what you want to think about first is the leading terms here. X times what is three x squared. Well, that's going to be three x and because you're dividing by two terms like I said earlier, your answer is going to appear on top of the second term first. Now, just like in regular long division, you're going to take that three x and multiply it by the x plus two individually. So here we go. three x times x is three x squared. Three x times two is going to give you six x. Normally at this particular point you will subtract. But here's one thing to keep in mind to make subtraction a lot easier. Change the sign. Three x squared plus positive, turn it in to a negative. The six x is positive, change that to a negative. Because this is what happens. Three x squared minus three x squared, that's completely canceled out. But two x minus six x is going to give you negative four x. Now, just like in regular long division, you bring down the next number, the next term. So we're bringing down the plus one. Same exact approach as we did before. X times what is going to give you negative four x. That's actually going to be negative four. Same thing, take the negative four, multiply by the x plus two. So we have negative four times x is negative four x. And negative four times positive two is going to give you negative eight. Now, just like we did before though, when it comes to subtraction, the easiest thing to do is to change the signs. So the negative four x becomes positive, the negative eight becomes positive. Negative four x and four x are canceled and one plus eight is nine and that is your remainder. So, I'm Jimmy and that is exactly how you divide polynomials.


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