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Alright, what I'd like to do is show you guys how to find the x intercepts of an equation.
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Given this polynomial x squared minus x minus 12 equals zero.
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The first thing the way that I like to go out to teach us is I like to go and look at
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whatever A, B or C is.
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Whatever we're doing with polynomial, there's a lot of different forms that we can use.
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So the main four things I want to find out which are the components.
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So when you determine if you guys remember the formula for our polynomial is A x squared plus B x plus C.
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So over here we have A equals 1, B equals negative 1 and C equals negative 12.
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So now if I want to find out what are the x intercepts, I need to find the values for my x.
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And since I have x squared and the negative x, I can't just use my regular solving.
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So what I'm going to do is I'm actually going to do factory.
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So one of the methods we look at is we say, alright, if you can find your A times C and your B,
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then find what two numbers are going to multiply to give you your A times C value and add
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it to give you B.
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Let me just go and explain that a little bit further.
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So A times C in this problem is going to be negative 1.
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A times C is going to be negative.
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I'm sorry, that's positive 12.
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No, it's a negative 12.
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And then add it to give you negative 1.
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So you need to look at the factors of negative 12.
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Let's see factors of negative 12.
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Multiply to give you negative 12, but add to give you negative 1.
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And which one notices if you can come negative 4 and 3.
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Therefore, then we have x minus 4 times x plus 3 equals 0.
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Now the important point for this is what you should notice.
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If you use foil techniques, which we've done before, you know, you do foil is back out,
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you will get x squared minus x minus 12.
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So all this is is you just took a trino meal and factored it, and detuned it from
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binomials.
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Now to find out what the x value is, if I wanted to solve for this x value, what I
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do is I have to divide my x divided by 3 on both sides.
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And obviously that can't smile and that's still equal 0.
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So therefore x minus 4 equals 0.
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And if I was going to do it the other way, I was going to solve for this one.
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I'd have to divide by x minus 4 on both sides.
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So therefore x plus 3 equals 0.
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This is also what we call the zero product property.
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Now I'd solve for x equals 4, x equals negative 3.
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So therefore to find the x intercepts of the equation, I know that x equals of the
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equation by factoring it, I find out that the graph crosses the x-axis and x equals
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4 and x equals negative 3.