how do you factor This is a topic that many people are looking for. star-trek-voyager.net is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, star-trek-voyager.net would like to introduce to you How to Factor any Quadratic Equation. Following along are instructions in the video below:
How to factor anything with x squared in it.
Is a quick three step process on how to factor any quadratic that’s actually actually factorable. The first thing you have to do when you’re given some quadratic that you have to factor is that if there’s something common to all of the terms take it out first it’s just gonna make your life. Easier then you have to look at what’s left if you’re left with x.
Squared. Plus. Something x.
Plus. Something. And it’s just a bear.
X. Squared. Then you can use product sum.
And i’ll show you how to do that if you don’t already know what it is but you may be left with something in front of the x squared like 2x squared or negative 5x squared plus something x plus something if that’s the case. You’re gonna have to use a little bit more complicated of a method. I’m gonna show you how to use decomposition.
But you may be familiar with another method some people use a box. Some people use a bunch of other tricks you can use to whatever you want. But i’m going to show you how to use decomposition because anyone can do it okay.
So let’s follow the process and do this for a few different things the first one that i want to do it for is x. Squared. Minus.
2x minus. 15. Is there a common factor among all the terms now x.
Squared minus 2x minus 15. This one’s missing an x. There’s no 2 or anything here so there’s nothing we can pull out of all of those there’s nothing common to all of them.
No next are we do we have a bear x. Squared. Yes.
We do it’s just x. Squared minus. 2x minus.
15. So here’s how you do that second step find two numbers that multiply to negative 15 and add to negative 2. As soon as you find those two numbers you can plug them right in to this well let’s figure out what those numbers are they’ve to multiply to negative 15 and add to negative 2 well what multiplies 250 to negative 15 negative 1 and 15 multiply to that but they add to positive 14.
So that’s no good about negative 15 and 1 those add to negative 14. That’s no good it’s been a give to what about negative. 5 and 3 those multiply to negative 15 and they add to a negative.
2 look at that those are the two they multiplies if negative 15 and add to negative 2 negative 5 and 3 negative 5 and 3 it’s actually that easy as soon as you find those two numbers cool someone’s done we got rid of our x squared. We’ve split it up into two separate terms. We’ve factored it ok let’s do this one start at the beginning.
Is there a common factor. Among all the terms. 3 2.
5. Nothing common among those is in a bear. X.
Squared. Yeah. It’s not so.
We’re gonna have to use this thing called decomposition here’s how you do that the first thing you do is find two numbers that multiply to this times. This now this is the only way that this new search is different from the old search you have to do negative. 5.
Times. 3. You want them to multiply to negative 15 and add to negative.
2. Now i rigged this so that it would be the same thing two numbers that multiply to negative 15 and add to negative 2 are obviously negative. 5 and 3 we already found it but because we have something in front of the x squared we have to do this and a bit tougher of a way what we do is we write that laughs that first term and that last term just as they are negative 3 x.
Squared minus 5. And we rewrite the middle term as these two here negative 2x as minus 5x plus 3x now see negative. 5 plus.
3 is negative. 2. But we’ve divided it up we’ve decomposed it get it and then once you get their factor.
The first two terms. What’s common to both of these well not much. Except for they both have an x in it.
And when you pull x out of that you’re left with 3x minus. 5. Notice that this is each of these terms.
But we took away one x from each of them. Then you factor the second two what’s common to these nothing. So it’s really just a 1 if it’s nothing and because we weren’t able to pull anything out we’re left with 3x minus.
5. Now we have 3x minus 5. In both of these terms.
So we can pull that it. And what are we left with well when we pull 3x minus. 5.
Out of this we’re left with x. And when we pull 3x minus. 5.
Out of that we left of plus 1. And that’s the factored form of that equation a little tougher because you have to decompose that middle term. Then factor the first two and second two terms want to do a couple.
More here is there a common factor among all the terms. Why yes. There is there’s a common five both of these are divisible by five and there’s an x in both of them we can pull out a 5 and an x from both of these terms when we pull it 5x from this we’re left with just a single x.
When we pull 5x out of this we’re left with just 2. We pulled it the x and we pull it 5 from there 10 divided by 5 gives us that oh look we’re already factored because there’s no x squared. Left that was easy finally.
Let’s do this. One is there a common factor. Among.
All the terms one half x. Squared minus. 1 2.
X. Plus. 12.
I don’t know well. Let’s see you know what i could pull out a half here and when i pull a half out of a half x squared. I’m obviously left with x squared.
When i pull out a half from negative 1 2. X. I’m left with negative x.
And when i pull out a 1 2 from positive 12. I’m left with positive. 24.
Now is a 1 like do i have a bear x. Squared. Yes.
I do if we remove that 1 2. Which we already factored out. We have x squared minus x.
Plus. 24. That we have to factor.
So. It’s just a bear. X.
Squared. We can use this product. Sum.
We need two numbers that multiply to 24 and add to negative. 1. That’s the number in front of x well we got to start reaming off pairs of numbers that multiply to 24 1.
And 24. Those don’t add to negative. 1.
Though so that’s no good that way negative 1 a negative 24. Those don’t work 2 and 12 multiply to 24 but don’t add to negative 1 negative 2 and negative 12 those don’t well those don’t add to negative 1 either what about 3 8 don’t add to negative 1 negative 3 and negative 8. Yeah don’t add to negative 1 4 6 multiply to 24 ah doesn’t add to negative 1 well negative.
4. And negative. 6.
That also doesn’t multiply to negative 1 you know what i’ve exhausted all the pairs of numbers that multiply to 24. This can’t be factored further. And you got to be on the lookout for that because you know what sometimes you just can’t factor things.
But before you write a bold statement like can’t be factored further. You should probably run through all the possibilities like i did these are all the pairs of numbers that multiply. 24.
And not a single pair adds to negative one that means you can’t factor. It further three step process follow it the old a factor anything you want music. .
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