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Alright, what I'd like to do is show you guys how to divide polynomials using long division.
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Long division is the exact same process and the reason why you guys learn it in such a young age
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was to go and find a process that you can pass the leaves.
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So if you remember the process, all we're going to do is apply that exact same algorithm step by step process
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into now using polynomials.
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So what we're going to do, we're going to take one large polynomial and divide it by another one.
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And what we're going to do is you're just going to work with the leaving term and you're just going to divide it into each one of these terms.
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So I'm going to say x divided into x cubed.
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So how many times does x go into x cubed?
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And you say it goes in there x squared.
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And the reason why I want to double check that is if I say multiply x squared times x, that's going to give me x cubed.
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So you're remembering when you're dealing with division, that's what you want to work with.
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When you divide in, you can always check your answer by multiplying your top number times what you just divided by.
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And double check, make sure you got your answer.
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So then you have two terms here though.
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You can't just multiply it by one, you have to multiply the term.
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So x squared times two is going to give you 2x squared.
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So now we go ahead and subtract, get our next row, that becomes zero.
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And I have 4x squared minus 2x is 2x squared.
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x goes in 2x squared, 2x times, and let's double check our answer, 2x times x gives me 2x squared.
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So therefore that is correct, that's going to work.
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Then 2x times 2 is going to give me 4x.
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Yes, and now go ahead and drop this down.
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Because remember this is going to be all fine now, you guys, if you guys remember,
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you guys keep on dropping this down and keep on subtracting.
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So therefore now I go ahead and subtract, this is going to give me zero.
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And then a negative 3x minus the positive 4 is going to give me a negative, a 7x.
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x goes into negative 7x, negative, 7 times, negative 7 times x gives me a negative, a 7x.
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I bring down my negative 12.
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When I bring down my negative 12, I say I have a negative 7.
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So the negative 7x2 is going to give me a positive 14.
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Where is my negative 14?
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Oh, that should be a, what?
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Pretty good, send.
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Oh, that should be a negative 14.
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I'm going to be there.
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So, it's right there.
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Negative 7 times 2 is going to be a negative 14, and then when I subtract these, I'm going to give a negative 2.
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Okay, because the memory you're extracting these, so that becomes a positive.
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I'm sorry, that's going to be a positive 2.
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W positive 14, negative 12 minus a negative 14, coming to positive 2.
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x now does not go into 2.
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So therefore, my remainder, we're not going to write the r2.
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So we're going to write plus remainder of 2 divided by x plus 2.
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So, and that would be your correct final form of your equation is, your final answer,
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just like old dividing, would be x squared plus 2x minus 7 plus the remainder over your divisive.
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So that's how you divide polynomial using the wrong division.