So in this case you factor out the x squared leaving you with 3x squared minus 2, okay? You take out the smallest power on x. You look for the smallest power of x that you have, okay? The first thing you want to do is to factor out the greatest common factor. If I say 3x to the fourth minus 2x squared and I asked you to factor this. The other sort of complicated thing I want to look at is, if we're dealing with negative exponents, okay? So say I want to factor this expression which has 3 different negative exponents. Like I said, you could foil all this out if you wanted to but it's going to be a lot harder and you're more likely to make mistakes than if you just make a simple substitution. Combining like terms what we have then is 3x-4 quantity squared, okay? So factoring a fairly ugly thing by making a substitution makes your life easier.
It doesn't really make any sense to introduce a different variable as our end product, so what we have to do is go back and take this u and plug it back in, okay? So this u is 3x-2. But if you look at it, our initial variable was x. They want to say, okay I factored it down, u-2.
#FACTORING EXPRESSIONS HOW TO#
I know how to factor this, this is just going to be u-2 quantity squared, okay? Be careful though because a lot of people want to end right here. So all we've done is we've taken something that's kind of complicated by making a substitution, a u substitution, I've turned it into something easy. Okay, we know how to factor this now, okay. 3x minus 2 squared just becomes u squared minus 4 times 3x minus 2 just becomes -4u and then the +4 is left down the end. Okay, by saying u is equal to 3x minus 2, I can then go back to this problem. So if you just introduce a new variable for whatever you're dealing with. And while I say I you as my substitution variable, you can do whatever you want but I highly recommend not using whatever variable is in your problem, okay? Because if you use x then you're going to get confused on what x is what and it'll get all confusing, okay.
#FACTORING EXPRESSIONS PLUS#
What we have is something squared minus something else times something plus 4, okay? And what we can actually do is make a substitution. Okay? But I want to show you a little bit of a shortcut that we can do in order to deal with this.
The most common approach to doing a problem like this is at least that students want to do is to foil everything out, combine like terms and then factor it down again. Factoring complicated trinomials, okay? What I mean by complicated is something that sort of looks a little bit different than what we are used to.
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