For week 9 of Math 10, my class is continuing the unit on polynomials however we are starting to get into factoring. Factoring is when you find the GCF or Greatest Common Factor that is shared between terms and the numbers in them and simplifying them by dividing them by the GCF. For example, the GCF of 9, 18, and 21 is 3 because that is the largest number that each of them can divide by equally to be simplified.
To begin we are going to start off with factoring a trinomial into simple terms. For this question we are factoring 12x – 8y + 16z. So to factor this trinomial, we need to find the GCF between these three numbers. Now 
off the bat you might know right away what the GCF is between these three numbers but when we get into more difficult polynomials, just looking at them is not going to be an efficient way of finding the GCF. So what I did is that I wrote down the factors of all of these numbers on the right. As you can see, the largest factor that they all share is 4 so that is the first step in finding the GCF. Next we look at if any of the terms share variables. In this case they don’t, all of them have different letters( x, y, and z) so our GCF is just 4. Once this is finished, we divide all of the terms by 4 and we wright our answer below. The last thing to do is to write the remaining equation (that has been simplified) on the right of the GCF and we end off with the final answer of 4(3x – 2y + 4z).
In this next example, we are going to do the same thing on a slightly different question. So with our question 5
GCF is to write all of our numbers and their factors down which I did on the right. I then found the largest factor that they all shared (which is 5) and we are done our first step in finding the GCF. Next we again have to find which variable that they all can be divided by or that they all share. As you can see, they all share the variable x and that is it. So we combine our variable and our number that we have found and our GCF is 5x. Once this is completed, write down 5x below our equation and then we divide all of our terms by 5x. We then write our result to the right of our GCF and we end up with 5x(x – 2y – 4z).