How to Factor
Question
Factoring is the reverse operation of
Hi my name is Bassem Saad, I'm an associate math instructor and a PhD candidate. I'm here for About.com to show you how to factor.
Tips for How to Factor

So recall that factoring is the reverse operation of the distribution property. For example, if we had this mathematical expression, we can factor it to get a new expression. We can then take this new expression, apply FOIL, or the distribution property, and show that these two mathematical expressions are actually the same.
Example of How to Factor

Let's take a look an example. The grouping method works whenever your expression has four addends inside of it. The first step is to look for the greatest common factor over all four addends. In this case notice that 2 divides into every addend and nothing else divides into every addend. So you know that your greatest common factor is 2. So you factor out the 2 and you get a new expression. In the next step you group pairs of the addends. The first two and the second two. For step three you want to factor out each of the pairs of addends. So notice in the first pair of addends you can divide out 2 into both terms and you can divide out x into both terms. That means your greatest common factor is 2x. If you divide out 2x you leave 5y - 7.
Additional Steps for How to Factor

We do the same thing for the next term. We can divide out 3 and that's it. So we factor out our 3 and we also have another 5y - 7. Notice that this group and this group are the same. So in the last step, we know after we factor out, we're going to have 5y - 7. We carry this 2 down to. And then when filling out the last set of parentheses we just look at the first terms 2x and the next term + 3. And now we know what the factor of the original expression is. So we've just seen how to factor by grouping.