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Review of the Methods of Factoring - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

The first step is to identify the polynomial type in order to decide which factoring methods to use. Next, look for a common term that can be taken out of the expression. A statement with two terms can be factored by a difference of perfect squares or factoring the sum or difference of cubes. For the case with four terms, factoring by grouping is the most effective way. This method is explained in the video on advanced factoring.

Alright, so whenever you are factoring a expression, there a lot of things you should look for. You should first and foremost always look for a common factor. So what I mean by that is, is there something that every single term has that we can take out to make our numbers smaller, okay? [IB] the smaller the number the easier the thing is to work with.
Next what you should look for is, is it a trinomial, a binomial or is that 4 terms. Okay, and how many terms there are dictates what your approach is going to be. If there are 4 terms that is a fairly sure sign that you are going to factor by grouping, and what you have to do there is pair up a couple of your things, factor out something from each of those and hope that you end up with the same thing so you can then factor it again.
If it's a trinomial, there's a number of different approaches. Maybe it's a prefect square, in which case you can factor quite easily. Sometimes, most of the time does not in which case you probably have a number of different ways to factor it. Some people just like using common sense in thinking about it, some people like a box method, some people like a diamond. There's all different ways of looking at it but the main thing is taking these 3 terms and factoring it down.
But lastly, if you have a binomial, if you have 2 terms, you're either going to be looking at the difference of squares. So you have something squared minus something else squared or the difference or sum of cubes. So is he have something cubed plus or minus something else cubed, and we have special formulas for each of those.
So basically, factoring. Always look for the or common factor to take it out and then let's have that, there's just a number of things we have in our tool box in order to factor it down even more.

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