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Discussion Prompt: Teach the class how to use the greatest common factor (GCF) to simplify a polynomial expression. Illustrate the concept with examples. Remember that teaching requires detailed explanation, as well as the actual math. In addition, create a similar exercise as you explained in the video for your classmates to try.
Videos can be recorded using any software or tool.
Substantive Participation Guideline: When responding to a peer’s exercise about factoring polynomial expressions, create a video demonstrating and explaining your thinking to support your answer.
Original POST DOES NOT NEED A response, ONLY PEER RESPONSES:
Peer (1) Jill
We will try to factor out the Greatest Common Factor (GCF) from the following 5b2-15b
First, let’s work on the numerical terms (5,15)
So, first I need to find out what two numbers when multiplied can give me 5, the answer is 1. Because in the multiplication table, there are no other numbers that when multiplied can give me 5, except for 1 and itself.
This makes 5 a Prime Number. Prime Number, is when a number can only be multiplied by 1 and itself. For example, 2, 3, 5, 7, 11, 13, 17, and so on, are also considered prime numbers. They only have two factors, 1 and itself.
Next, what numbers when multiplied can give me 15, the answer is 3, because 3*5=15.
Therefore the GCF is 5b
Now let’s work on our numerical and variable factors together 5*b*b-3*5*b.
My answer is as a factored expression is 5b (b-3)
so, 5b2-15b = 5b(b-3)
Peer (2) Joann
https://westcoastuniversity.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=1ec6fbf9-45b7-469e-aa17-ad5e017647a0 (Links to an external site.)
For this week’s discussion, we will be tackling the greatest common factor (GCF) and how it is used to factor out or to simplify a polynomial. But before we proceed to the main process of doing it, let me first give you some information about the terms that we will use along the way. This is to ensure that we will have a clear understanding of the whole concept.
So first, what is a factor? This refers to the quantities that you use to multiply together in order to create a product or a polynomial. For example, to get the product of 12, you need to multiply its factors, which are 3 and 4. In terms of polynomials, you can get the product of x2+5x+6 by multiplying the factors (x+2) and (x+3).
On the other hand, the greatest common factor (GCF) pertains to the highest monomial that is a factor of each term in the polynomial. For example, to find the GCF of the polynomial 40×3+10×2+20x:
First, you find the GCF of the coefficients 40, 10, and 20. Is there any number that we can use to divide these numbers evenly? YES! 10.
(40/10=4) (10/10= 1) (20/10= 2).
Second, look at the variables and check if you can factor out the variables in each term. Based on our example, the variables can be factored out since all of them have at least one x, hence, we can factor out x.
Now, you just need to combine the GCF to obtain the coefficient and variable, which is 10x. You now have the GCF of the polynomial 40×3+10×2+20x.
Furthermore, now that we are aware of getting the GCF of a polynomial. Let’s now discuss how to use it in simplifying a polynomial expression. Specifically, one of the ways of simplifying polynomials is through the use of the distributive property. And to realize it, we need to use its GCF.
Using the example that we used a while ago, which is 40×3+10×2+20x, we will use GCF to simplify it.
First, divide each term using their GCF:
(40×3/10x= 4×2) (10×2/10x= x) (20x/10x= 2)
Then write the combine these terms together, with their GCF in a distributive form:
Therefore, the factored/simplified form of our example is 10x (4×2+x+2).