Another Tuesday Post

If you're reading this it means you've already gone through the other blog post for today and checked your answers for Friday's questions along with the step-by-step pictures.

P.S. - Roscoe says hello:

Now that we (hopefully) have a good understanding of how to find the GCF of two numbers by using prime factorization, let's take a look at polynomials.

First, let me explain what a polynomial is. A polynomial is an algebraic expression with more than one term. We did a lot with polynomials back when we were simplifying expressions. 3ab is a polynomial - it says "3 times a times b" because they're all right next to each other. 6a³b and 4a²b are also polynomials. 

So... what does this have to do with GCF, you might ask? We're going to be finding the GCF for polynomials, using prime factorization, just like we did with regular numbers.

Let's take those two polynomials from above (in red) and first find the prime factorization of each. We do this by breaking down any regular numbers in the polynomial into its prime factor. Then, for all the variables, just write them out (take them out of exponential form):

It's kinda like take a puzzle apart. Now, the second polynomial:

 Now we can compare the two prime factorizations:

We have a few matches. One 2 on both sides, 2 a's on both sides, and a b on both sides. Multiply your matches together, and now we have the GCF:

The GCF = 2a²b

This example is also given in your textbooks on pg. 191. 

Please watch the following video from Khan Academy only until 2:31:

https://www.khanacademy.org/math/algebra/polynomials/multiplying_polynomials/v/factor-polynomials-using-the-gcf 

As usual, if you have any questions please leave me a comment. Using this information try pg. 193, 21 - 24 and 37 - 40. Please turn in what you have to your sub.