FACTORING EXPRESSIONS HOW TO
FACTORING EXPRESSIONS PLUS

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.

Factoring expressions