At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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.
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?
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.
And then do you subtract the 1x to the 3x?
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 :)
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!