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Alright, what I'd like to do now is show you how to go and do this factory in here, factory.
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First thing I want to do is I want to see if I can pull anything out.
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And I look at this and can I do anything out?
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No, there's no common number of tuning in to one of those terms.
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So the next thing I go and look is there's no perc square or I don't want to complete the square.
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So before I go and use a project form, I want to see, well, can I go ahead and still go back to this?
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So I do my A times C, which is two times negative three, which is a negative six, and my B, which is five.
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So I look at my numbers and say, what two numbers multiply, give me negative six, which means negative one and positive six, what add up to give me five.
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Now, there's going to be three different ways I'm going to show you guys how to solve this.
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Three different ways to find the middle terms.
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The first way is we know our two factors are negative one and six.
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All right?
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The first way we can take our two front terms and I can write two X minus one times two X plus six.
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Then from here, I just bet throughout what terms they have in common.
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So here I can't point anything out, but here I can pull out a two.
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So I'm like with two X minus one times plus two X plus three.
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So therefore I have X equals one half and X equals a negative three.
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That's the first method.
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You just kind of take it with the A, what the A is without the square, putting it in both binobiles, and then factor out what they have in common.
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Another method is to take your two terms and rather than writing the B term, take your two terms in there.
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So I could write, so that's method one, you could write two X squared, minus one X plus six X minus three.
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So instead of writing my B term, I wrote what my two factors are.
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Then now what I'm going to do is I'm going to split this up into my two binobiles and I'm going to factor out what I can.
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Here I can factor out a X, so I'm left with two X minus one.
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Here I can factor out a negative three.
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I take factor out a negative three from there I'm left with A, X, yes a positive.
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I don't want to take out that three, I want to take out A.
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I don't affect throughout a positive three, I'm sorry.
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If I affect throughout a positive three I will left with two X minus one.
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So now that I've factored a positive or a positive three, now I have two X minus one, two X minus one.
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Now I can factor out this, as we call factor by grouping.
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Now I can factor these two out, so I can factor out two X minus one and I'm left with an X plus three.
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Again, same thing.
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X equals one half, X equals negative three.
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In the final way I can do this, if either of those don't really make sense to you,
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you can always go and represent it as an area.
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So I can say I'll make a box and I'll put my A term, my C term, A term goes in the top left corner
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and my C term goes in the bottom right.
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I put my two factors there with were negative one X and negative five X.
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And then you simply just go ahead and say, no that's not negative five X.
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And you simply just say, well where did my two areas go?
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And what is, it appears the area, what are the sidelines?
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So you say, this is two X, this is one X.
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Two X times what you do three.
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Two X times what gives you six X and you say positive three.
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And two X times what gives you negative one X?
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Or one X times what gives you negative one?
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You say, one X one.
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Then you notice those again are the same factors.
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Two X times one times X plus three.
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So my answer is X equals one half, X equals negative three.
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So there's three different ways you can finish off the problem.
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There's three different ways you can finish off the problem.
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When you're factoring a problem, when A is greater than one.
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All right?
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Yes.
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How do you get X times two X minus one?
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Who has three times two X minus one?
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Right there in like the middle problem and the second step.
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This one?
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How did you get that from the problem?
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Okay, what I did was I took our two factors,
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which, remember, we did the dom problem.
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Yeah, I get all that high with the equation, but like...
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We said these are two factors, right?
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So what I did was I took our two factors and I said negative one was here,
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and then six was there.
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So what I did was I just wrote that in instead of our middle term,
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I wrote down one or two factors where...
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No, I get that.
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Because five X, and then what I did was now I just split them up
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and I factored this and I factored this.
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This, factoring it, I can take out our next.
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Here, factored this and I can take out a three, huh?
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Why would you take out a next?
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Because these both share an X, so you can take it out.
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So I took out an X. These both share a three, so I took out a three.
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Then I looked at this whole long equation.
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This is my real wife now, I'm talking to you.
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You took it out.
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Because when I took it out, now I have a two X minus one in both of them, correct?
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So then what I did was I took out a two X minus one.
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And when I take out a two X minus one, I'm left with an X plus three.
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That's where I got the plus three.
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Okay?
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That's five.
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So that's how you find the root solution zero.
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Factored sub-quite-of-function, when you have a quadratic form,
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when A is greater than two.
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homework.