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Dividing Polynomials - Concept
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Long division can be used to divide a polynomial by another polynomial, in this case a binomial of lower degree. When dividing polynomials, we set up the problem the same way as any long division problem, but are careful of terms with zero coefficients. For example, in the polynomial x^3 + 3x + 1, x^2 has a coefficient of zero and needs to be included as x^3+ 0x^2+3x+1in the division problem.
Alright guys we're going to start this video with a little bit of a throw back, think back to like fourth grade or whatever when you learned long division and this is the process you do. Your teacher shows you a problem like this and you set it up where 15 is outside the little division sign 2735 is inside and then what you do, by the way this is important don't just gloss over this I am showing you this for a reason, you think about how many times this 15 go into 27, it goes once then you subtract and you get 1, 2 and you bring down this next term and you try to think about how many times does 15 go into 123 and that's 8 and what you do is 8 times 15 to see what goes here and it's a 120 blah blah. You guys know how to do this, I'm almost done but then I do want to show you an important thing of how this applies to dividing polynomials.
You're going to use this exact same process, the last thing you do when you're dividing using long division is you write your reminder on top of that guy. You would write 5, 15ths, I'm going to reduce that to one third. Remember this process how you subtract things, bring down the next term it's going to be the exact same process you use when you're dividing polynomials using long division. You're going to see once you start going into these problems how to go through it when these are x's and x squared instead of actual numbers.
But the important thing to think about is the process that you guys have known for a long time. You start by looking at how many times does 15 multiply into this first term, you write your answer there, multiply and then subtract bring down your terms as you go. The last step is to write your remainder on top of this thing here. Be really careful with that, use that process for long division of polynomials.
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Sample Problems (3)
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Problem 1 4,972 views
Divide:2x³ − 13x² + 17x + 12 by x − 4
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Divide:(x³ − 13x − 12) ÷ (x − 4)
Problem 3 3,264 views
The volume of a room can be represented by V(x) = x³ + x² − 6x where the length is x − 2. Find expressions for the width and height.