Thursday January 17th:
Today in class, we started by going over the homework we had from Wednesday which was on page 234, numbers 13-29 every other odd. After we finished that, we took notes about graphing with factored polynomials. The first example that was put on the board was as follows:
y=(x+3)(x-7)(x+6) ---------> From this equation, we learned that the x-intercepts can be found by taking the opposite of each number and putting it in point form. In this equation, the x-intercepts would be (-3,0), (7,0), (-6,0). For a lot of the class, we were all up at the board doing examples of problems.
The next part of class was spent going over long-division and we learned that:
dividend/divisor= quotient+remainder/diviser
An example of this is:
x^3+2x^2-5x-6/x+1
x^2+x-6 <---------quotient
---------------------
x+1 |x^3+2x^2-5x-6
-(x^3+1x^2)
------------------------
x^2-5x
-(x^2+x)
-----------------
-6x-6
-(-6x-6)
------------
0 <---------remainder
Here is a video that goes over some basic problems involving long division: http://www.youtube.com/watch?v=l6_ghhd7kwQ
The homework for Friday was on page 245, numbers 9-10.
Friday January 18th:
On Friday, the majority of class was spent learning about synthetic division. After going over the long division homework, we took some notes from the board. We learned that synthetic division is a short cut that works when dividing by an x-constant. [ x+c= x-(-c)]
Here is an example of synthetic division that we did in class:
3x^4-8x^2-11x+1/ x-2
The coefficients are: 2⏐ 3 0 -8 -11 1
6 12 8 -6
-----------------------------
3 6 4 -3 -5 <------remainder
= 3x^3+6x^2+4x-3-5/x-2
We also learned about the remainder theorem which means that if you plug in the 2 from the example above into the equation, you will get the remainder (-5).
One thing that is very important to remember is that synthetic division only works in certain circumstances. You can't use synthetic division if the "x" in the denominator is squared.
This is a video that shows an example of synthetic division: http://www.youtube.com/watch?v=bZoMz1Cy1T4
The homework for Wednesday is on page 245, number 10, 11-17 odd.
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ReplyDelete(sorry making a few edits)
ReplyDeleteI really thought you described the process well! Instead of just stating it you gave examples which I really liked, so good job doing that! I also liked how you put the note about the remainder theorem because I often forget that short cut. It was also a huge help because I was sick most of this week when we learned it, so it's a very nice guide to catching up. Nice post, Allie (:
This is looking very good, Allie! I really liked the explanation of what the different types of division are and what they are used for! It was really helpful to see the visual examples. Possibly add in a picture for a better visual understanding? Overall, well done!
ReplyDeleteThe visual components and the layout of the problems are very helpful to me, and I liked the way in which you marked them. Though division with polynomials can seem a daunting challenge at first, you really emphasized the crucial steps for success in this subject.
ReplyDeleteI thought that you did a really good job of remembering the little details, like how synthetic division would only work in certain circumstances; I usually forget those kinds of things so thank you for reminding me. I was a little confused about the first example of division that was in the first part of your post, but eventually figured it out. Great job!
ReplyDeleteI agree with everyone, the details in this post are very well covered. Solid explanations to go along with examples and an interesting video. The suggestion I would have would be to make it a little more creative (something hard to to with math) other than that, great work.
ReplyDeleteok the internet is annoying me so i'm not sure if my comment already loaded, but i'll just say what i said before. i really like this! it is clear and simple, and i'm definitely going to use it for review for our test on friday. thank you for posting the homework questions, too. now i can go back and practice. and thanks for talking about the remainder theorem, i would have completely forgotten about that and/or what it meant. nice job :)
ReplyDeleteAllie, your post describes well what we covered in class. You've done a nice job showing examples (and it's impressive that you got everything to line up by typing)! Describing some of the process associated with division would have enhanced your post - some steps, tips, or "how to" information. I was thinking of this mainly for how to determine the parts of the quotient in long division and when to include a place holder. That said, the videos you chose do cover this nicely. I liked that you included the homework - this lets everyone know exactly where to look in the book for more information and examples.
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