Greatest Common Factors - Concept
We have rational functions whenever we have a fraction that has a polynomial in the numerator and/or in the denominator. An excluded value in the function is any value of the variable that would make the denominator equal to zero. To find the domain, list all the values of the variable that, when substituted, would result in a zero in the denominator.
Alright guys, one of the most important concepts you're going to be learning in your Algebra course is how to factor. Factoring is like undistributing, so sometimes when you're working with factoring or undistributing you're going to be looking for what's called the greatest common factor a lot of the times we just call it GCF.
The greatest common factor or GCF of two or more expressions is the greatest factor that divides evenly into both expressions. I have a couple of examples for you because a lot of times words are kind of tricky but the Math stuff isn't so bad.
Like for example if I have 3x take away 15, and I want to like undistribute that and I'm giving you a hint here I'm going to have 3 times something in parentheses. Well 3 times what gives me 3x? It's 3 times x and then 3 times what gives me -15? That's -5. Check it out what I've done is like undistribute if I thought of this is my original problem I could distribute to get to this answer.
Here's another example of what I'm talking about. If I have this difference and I'm asking you to undistribute using 2x, 2x times what gives me 8x squared well let's see it's going to be 4x right? Because I need 2 times 4 to give me eight and then I need x times another x to give me the x squared bit, then I still need this minus 2x business, so in my parentheses I'm going to write minus 1. It's really important to have that there so that when I will, if I were to distribute I would have 8x squared take away 2x.
This is called factoring it's also like undistributing and these things that are outside the parentheses that I provided for you, those are the greatest common factors so in some of your homework problems you're going to be asked to find the greatest common factor that's going to be your first step. Later on you're going to be asked to factor which means pull out the greatest common factor and do this undistributing bit, so a lot of times this isn't given to you but if you can look at these original problems and think "okay what multiplies into 8 and also multiplies into 2 okay that's going to be 2 what multiplies into x squared and also multiplies in the x, that's going to be 1x that's how it got 2 times 1x." Same thing here, what number multiplies into 3 and 15 negative 15 that's the 3 and I don't have an x term that goes into both of those. So what you're going to be doing in some of your early factoring homework is practicing finding the greatest common factor. What you want to do is look at the constants, 3 and 15 think about those, and then after you're done with that look at the variables like here I only have one variable I didn't have to do it but here I want to think about how many x's would multiply into x squared and also into x. That's how you can approach looking for the greatest common factor of two or more expressions.