Unit+9

**Unit 9** In Unit 9 we begin exploring polynomials and factoring. Remember that a __polynomial__ is a many term expression. Each term in a polynomial is separated by either an addition or subtraction.

Here is another example: 3x+1

This is a 2-term polynomial called a __binomial__.1-term polynomials are called __monomials__.3-term polynomials are called __trinomials__.Beyond 3 terms, we give them the general name n-term polynomial. In this unit we add/subtract, multiply, and factor polynomials. First, addition/subtraction of polynomials and determining the degree of the polynomials Review my notes thoroughly and then view a great video on how to add/subtract polynomials if you need additional help. You can view the video by clicking on this link. @http://www.khanacademy.org/video/addition-and-subtraction-of-polynomials?playlist=ck12.org%20Algebra%201%20Examples

==== Section 9.2 we begin multiplying polynomials using the distributive property method and paying close attention to some special cases of binomial multiplication. We learned that there were 3 special products and those can be reviewed in our notes here. ====

Here is the worksheet on factoring out the GCF [[file:GCF factoring worksheet.pdf]]
In Section 9.3 we learned how to use "double distribution" in what we call the FOIL method. That looks something like this...

FOIL is just one way to multiply binomials. We then practiced using both the distribution method and the FOIL method on this worksheet, which you completed for homework and/or extra credit.

I clumped section 9.4 in with the other sections since it seemed kind of redundant. So, we'll move onto Section 9.5. In Section 9.5, you began factoring polynomials, first by factoring out the GCF. Remember the GCF is the greatest common factor. If you need some review, you can look at my notes.

But wait, Mr. Burns!!! What happens if we need to factor and there is no GCF? Well... then we must use some other methods of factoring. Hence, the topic of section 9.6, factoring special polynomials. There are two types of special polynomials that we covered in class: 1. Perfect Square Trinomials 2. Difference of Squares (SEE VIDEO BELOW FOR A REFRESHER)

media type="custom" key="17573730" align="center"

Each requires you to recognize what type of polynomial it is and then following some simple basic steps to factor. Are the terms "perfect squares"?

Then what do we do? Well...check out my notes to review. Your homework worksheet can be downloaded here as well>

There's a great website to help you with factoring explanations and practice. You can get there by clicking here.

So what happens when there's no GCF and the trinomial isn't a Perfect Square Trinomial? Well... if a=1, then we look for "factors of c that add up to b". The notes on this method can be found here if you need them. If a is not equal to 1, then we use the "Split the Middle method". Both methods can be found in the notes on section 9.7

Our worksheet and Extra credit pages are really good practice for factoring. You can download both of those pages if you need extra help.

In the last section of Unit 9, we pull everything together and discover WHY we've spend so much time learning how to factor. We learned that we can use the factors to solve a quadratic equation. By applying the "ZERO PRODUCT PROPERTY" and setting each factor equal to zero, what we find is where our graph of our quadratic (parabola) crosses the x-axis. This can be handy.

Check out our notes here. After reviewing the notes on 9.8, I want you to factor and solve the quadratic y=2u^2-9u=-9. (Remember to set it equal to 0). You should get something like [|this]. Now go the Grapher Program on your computer and type in the quadratic equation. Where does the parabola cross the x-axis. It should be at the x-values that you got when you solved. Is it?