Question

Help for a medal??

Answer 1

Identify the factors of x2 - 4x - 21.

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

B will be 4, A will be 1.

Answer 7

Is this clear to you?

Answer 8

Yeah, so far it is

Answer 9

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?

Answer 10

2 x-intercepts?

Answer 11

That's exactly correct!

Answer 12

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?

Answer 13

No, I don't sorry.

Answer 14

That's no problem at all.

Answer 15

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

Answer 16

Yeah, I have

Answer 17

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)

Answer 18

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

Answer 19

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

Answer 20

We need to go from your formula into factored form.

Answer 21

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.

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

Not quite.

Answer 28

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

Answer 29

So I cross them out then?

Answer 30

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 :)

Answer 31

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

Answer 32

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

Answer 33

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?

Answer 34

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

Answer 35

That was an example.

Answer 36

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

Answer 37

Yeah, haha it's okay.

Answer 38

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

Answer 39

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.

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

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.