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Identify the factors of x2 - 4x - 21.
Hi. To get the factors of x^2 - 4x - 21, let's put this equation into factored form.
To start, please identify the a, b, and c components of this quadratic equation.

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Alright, would the A be x^2, B=4x, C=-21
Very close, but more precisely, A and B will need to describe the coefficients of the x factors.
B will be 4, A will be 1.
Is this clear to you?
Yeah, so far it is
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?
2 x-intercepts?
That's exactly correct!
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?
No, I don't sorry.
That's no problem at all.
Have you been taught about FOIL or expanding something that looks like: (x+1)(x-1)?
Yeah, I have
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)
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
Do you see how that matches the shape of your formula?
We need to go from your formula into factored form.
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.
Am I being clear? Please let me know if I'm being confusing
No I understand. It's just a little more difficult for me to follow since this is all in text, but I still understand.
Great. So let's look at your equation: x2 - 4x - 21
Let's learn what we know about FOILing and try to work backwards.
|dw:1433976603608:dw|
|dw:1433976690825:dw|
And then do you subtract the 1x to the 3x?
Not quite.
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
So I cross them out then?
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 :)
|dw:1433976867455:dw|
Let's start with trying to get the x^2 into our factored form. How can I make X^2 separating the X's?
We start off by setting up our two factors: (X)(X) Multiplying these two now would give us X^2.
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?
Sorry, I think I am being unclear. That is not the answer to your problem: x2 - 4x - 21
That was an example.
Oh. Sorry again. I see what you mean. Text is really hard today for some reason.
Yeah, haha it's okay.
We're basically trying to take X^2 + 4X + 3 and shove it into (x + something)(x + something) form.
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.
We still have to take care of the 4X and the +3.
Notice, when you do Inside and Outside of Foil, you get: a * X + b * X. Which can be written as (a + b)*X.
So our a plus our b has to equal the coefficient of X (the B value) in our expanded equation: x^2 + 4X + 3
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.
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.
Does this make any sense?
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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