How to Divide Polynomials Using the Box Method

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Dividing polynomials using the box method will require you to think about the total number of polynomials you have. Divide polynomials using the box method with help from a professional private tutor in this free video clip.

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Video Transcript

Hi, I'm Rachel, and today we're going to be going over how to divide polynomials using the box method. Let's say, we have the polynomial, three-X cubed, minus five-X plus seven. And we want to divide that by the polynomial, X minus 2. There's two ways to do this. One is long division and the other is synthetic division, or as we like to call it the box method. I find this one to be the easiest. All we do is we take this number, X minus, whatever that number is and we put it in a box. So, in this case, it's two. Remember that it's X minus whatever number. So that if was to be X plus two, you'd actually have to use negative two. But this case, we're o.k. because it's subtraction, we can put the two in the box. Then, we line up the other numbers that are at the coefficients from this problem. The tricky thing to remember here is that you have to do in descending order if exponents. And if you skip an exponent, like here, it goes from X cubed to X to the one, there's no X squared. So, we have to put a zero in that place because there's no X to the second power. A zero there, the next number is negative five and the next number is seven. So, we have all the coefficients. Now, we're going to do this cool thing called the box method. The first number, you just bring down, it's three. Then, you use a number in the box and you multiply it with the number here. Two times three is six and then, you take that and you add it to the next number up here, plus zero. You get six plus zero is six, so the next number is six. Then, we do the same thing. Two times six is 12, we multiply that, I mean, we multiply the two and the six and then, we add it to the negative five to get seven. 12 minus five is seven. Then, we just do it again. Two times seven is 14 and then, we add it to this number, 14 plus seven is going to be 21. Now, we have gone through all the numbers and all we do is, start with next exponent after this one. So, this is X to the third. So, we're going to go X to the second. So, you just do three-X to the second plus six-X plus seven. And then, we still have the 21 left. So that becomes the remainder. And we put that over the one we divided by, the X minus two, 21 over X minus two. And that's the answer, it magically turns into that using the box method. I'm Rachel and thanks for learning with us today.


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