The most important thing that I have learned this week in Math 10 is how to factor polynomials by removing the greatest common factor. Factoring a polynomial is when you turn it into a multiplication that shows the numbers which when multiplied together will result in the equation that you started with. Removing the greatest common factor is a good way to do this because the greatest common factor is the largest number and/or variable that can be multiplied into each of the monomials that is part of the polynomial. Removing the greatest common factor allows you to find out which other other factors are involved because they will multiply with the greatest common factor to result in the original expression. This was a very important and extremely useful concept to learn and understand because it is the way that you can easily find the polynomial before it has been expanded, when given the expanded version, which is the opposite of what I knew how to do before and therefore allows you to be able to convert polynomial expressions both to and from expanded. This is also an important skill to learn because before learning this, I only knew how to find the greatest common factor of numbers, but now I can find the greatest common factor of values with variables involved which is a lot more useful because you can find the greatest common factor of more terms that way.
Step 1: In order to factor polynomials by removing the greatest common factor, the first step is to be able to find the greatest common factor between the monomials involved. Finding the greatest common factor works the same in polynomials as it does with regular numbers, which is that it is the highest value that can be multiplied into both/all of the numbers or values in the equation. This works the same with variables, so for polynomials, the only difference in finding the greatest common factor is that you have to consider the variable factors as well as the number factors.
Example of finding the greatest common factor of polynomials:
Step 2: After you have found the greatest common factor, the next step to factoring the polynomial is to remove the greatest common factor, which means to put it outside of the brackets to be multiplied by the left over factors for each monomial. This is the step that changes the factorization into a multiplication, which when multiplied would create the expanded polynomial expression. To find what goes inside the brackets, you have to find what is multiplied with the greatest common factor to create the original value given, for each monomial. After doing this, you have found the factorization of the polynomial.
Example of factoring the polynomial by removing the greatest common factor:
Here is another example that we can factor by using these steps:
Step 1. First of all we find the greatest common factor. To do this we find the greatest common factor of 10 and 25 as well as of 
Step 2. Next we find the remaining factors that are left over after we remove the greatest common factor, 5x. To remove the greatest common factor we move it to the outside of the brackets, keeping the remaining factors inside the brackets. We can find the left over factors by dividing each side by 5x. This will give us 2x + 5 as our left over factors because when we multiply them with the greatest common factor, 5x, we get the polynomial expression that we started with.
