Help for a medal??

- anonymous

Help for a medal??

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- schrodinger

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- anonymous

Identify the factors of x2 - 4x - 21.

- anonymous

Hi. To get the factors of x^2 - 4x - 21, let's put this equation into factored form.

- anonymous

To start, please identify the a, b, and c components of this quadratic equation.

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- anonymous

Alright, would the A be x^2, B=4x, C=-21

- anonymous

Very close, but more precisely, A and B will need to describe the coefficients of the x factors.

- anonymous

B will be 4, A will be 1.

- anonymous

Is this clear to you?

- anonymous

Yeah, so far it is

- anonymous

Great. Now, we know that the formula you wrote is a parabola since it's highest term is the x^2. This graph will take the shape of y=x^2 which is a parabola. Parabolas have how many x-intercepts?

- anonymous

2 x-intercepts?

- anonymous

That's exactly correct!

- anonymous

So when we go to factor your equation, we know that we're going to only have two pairs of x intercepts.
Are you familiar with the factored form of a parabolic function?

- anonymous

No, I don't sorry.

- anonymous

That's no problem at all.

- anonymous

Have you been taught about FOIL or expanding something that looks like:
(x+1)(x-1)?

- anonymous

Yeah, I have

- anonymous

Great. So the idea is, the formula you gave me
Ax^2 + Bx + C is called expanded form. That's because all the terms are out in the open.
We need to get your Ax^2 + Bx + C into factored form. Factored form looks like:
(x + j)(x + k)

- anonymous

So if I use FOIL on an example:
(x + 3)(x + 4)
I get: x^2 + 3x + 4x + 12
Which equals: x^2 + 7x + 12

- anonymous

Do you see how that matches the shape of your formula?

- anonymous

We need to go from your formula into factored form.

- anonymous

We need to go into factored form because, for example:
(x+1)(x+2)
Your factors here are x+1 and x+2. And that is the answer to your problem :) So I need to show you how to get these factors.

- anonymous

Am I being clear? Please let me know if I'm being confusing

- anonymous

No I understand. It's just a little more difficult for me to follow since this is all in text, but I still understand.

- anonymous

Great.
So let's look at your equation: x2 - 4x - 21

- anonymous

Let's learn what we know about FOILing and try to work backwards.

- anonymous

|dw:1433976603608:dw|

- anonymous

|dw:1433976690825:dw|

- anonymous

And then do you subtract the 1x to the 3x?

- anonymous

Not quite.

- anonymous

I asked a question similar to this, and the helper said that you cross them both out, when I remember you having to add or subtract them

- anonymous

So I cross them out then?

- anonymous

Sorry, I am unsure what the helper was doing for that particular problem. I have guesses, but I don't want to make something up and confuse anything :)

- anonymous

|dw:1433976867455:dw|

- anonymous

Let's start with trying to get the x^2 into our factored form. How can I make X^2 separating the X's?

- anonymous

We start off by setting up our two factors:
(X)(X)
Multiplying these two now would give us X^2.

- anonymous

Yeah, I get that part but what I am confused by is what to do after. So you got x^2+3x+1x+3. But what do you do afterwards?

- anonymous

Sorry, I think I am being unclear. That is not the answer to your problem:
x2 - 4x - 21

- anonymous

That was an example.

- anonymous

Oh. Sorry again. I see what you mean. Text is really hard today for some reason.

- anonymous

Yeah, haha it's okay.

- anonymous

We're basically trying to take X^2 + 4X + 3 and shove it into (x + something)(x + something) form.

- anonymous

To do that, we start off with our nice template.
(x + a)(x + b)
If we foiled this out now, our first term would be X^2, which satisfies the X^2 in our expanded equation.

- anonymous

We still have to take care of the 4X and the +3.

- anonymous

Notice, when you do Inside and Outside of Foil, you get:
a * X + b * X.
Which can be written as (a + b)*X.

- anonymous

So our a plus our b has to equal the coefficient of X (the B value) in our expanded equation: x^2 + 4X + 3

- anonymous

And now we look at our last term which ends up being a*b.
So our a*b must equal C in the expanded form.

- anonymous

So when choosing a and b values for your factored form:
(X + a)(X + b)
You must satisfy two constraints:
1) a * b must be C.
2) a + b must be B.

- anonymous

Does this make any sense?

- anonymous

Yeah. I can actually handle the problem from here. Thank you for your time! Since you spent a good amount of time with me, I'll give you a medal and fan!

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