On Thursday we were introduced to Graphing With Factored Polynomials
y= (x-2)(x+7)(x-5) --> Degree 3 because there are 3 x's, also meaning that it will cross the x axis 3 times.
so then we found that in this problem it crossed the x axis at (-7, 0), (2, 0), (5, 0) and we were all like "daanngg its so easy to see the x-intercepts when the problem is factored!!!!!"
But just to make sure everyone remembers why we thought it was so easy, lets do it out.
(x-2) - then we ask ourselves "hmm..what do i plug in for x to make this come out 0? OH A 2!!! "and thats how you got (2, 0).
(x+7) "hmmmm...how do i get to 0???" OH a -7!! --> (-7, 0)
(x-5) "Oh I get it, I get it, a 5 would make it zero.Wow, this is so much easier when factored!"--> (5, 0)
My x-intercepts are (2, 0), (-7, 0), and (5, 0) because when I plug them in I get 0.
Next in class we went up to the board and drew some examples:
#1
#2
#3
Then we were introduced to Long Division.
1st we recalled doing long division with numbers.
This is just a general idea of what your answer should look like. The quotient is what you get after you do the long division
And if you're having a hard time remembering how to do long division with numbers here's a video/song that will help you understand how to do it in a catchy way.
http://www.youtube.com/watch?v=R_cqrdZNmr0
Then we tied long division in with polynomials.
Here's an example:
1. x times what gives you x^2 (put that answer on top of the dividing bar.)
2. multiple the answer you got with the leading term on the outside of the dividing bar. (x time x) **You should always get the same as the first term on the inside of the bar, so they cancel out**
3. 1 times x^2 = x bring that answer down next to the x^2
4. subtract
5. repeat with other terms of the dividend
Another example:
That was the end of Thursday's class.
Friday, we reviewed a lot of long division but then we were introduced to Synthetic Division.
**** Synthetic Division only works when you are dividing by x-c [x+c = x-(-c)] ****
two key things to remember during synthetic division are:
1.write down coefficients.
2. flip the sign of the divider.
http://www.youtube.com/watch?v=fdUQuQ-AYM4
Hopefully that video helped.
Here's one last example:
ok thxxx c u thursday!! (cuz we gon get a snowday 2morro) pce out gurlz 'n boiz
I liked the casual writing it was funny! And the videos were really funny too. go you for finding that synthetic division one. But the color that was used to highlight stuff was really hard to read the numbers. But it's okay because I used a bad color too. YAY Colbzidoo
ReplyDeleteI have to agree with Phoebe that the casual writing was funny, but maybe distracting from the core message of the post. Not that I didn't enjoy it. Also the colors were pretty janky, but when you're writing it, the background is white so I can see how it would change to create an undesired result: jankiness. Good job, and don't forget, drop it like its hot.
ReplyDeleteNice job Colby! I really liked how you used drawings on a whiteboard to illustrate how to do the problems. That was so helpful for me. Also your step by step explanations under some of the drawings really helped make the process clear. I agree with Phoebe and Austin that your casual writing made the post funny and easy to read. And of course, that video was hilarious. All in all, awesome post!! :)
ReplyDeleteColby, your post has a very casual voice, which seems helpful to some but distracting to others. You did a nice job of explaining the connection between the factors of a polynomial and the x-intercepts of its graph. Your white board examples provide nice visuals. Unfortunately, the graph in #2 is incorrect. When the leading coefficient is negative and the degree is odd, the graph starts high and ends low. With long division, your examples and step-by-step description demonstrated the process well. The synthetic division video outlines the process well, however I did remove your link to the Snoop Dogg video as the lyrics and references are inappropriate. Overall, your post summarizes the classes well.
ReplyDelete