Please respond to both POST1: and POST2: in at least 200 words each. I have also included the professors original post only for reference in answering the students post.
Professors original post:
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For this discussion, complete the following tasks:
- Write your own polynomial division problem.
- Solve it using long division and synthetic division.
- Discuss which method you think is better for your example and why.
- In your responses to peers, compare and contrast your thoughts in analyzing their examples.
Try this notation to make it easier to read:
e.g. Find (x^2+4x-8)/(x-2) using both long and synthetic division
___x + 6____________
x – 2 ) x^2 + 4x -8
-(x^2 – 2x)
6x – 8
-(6x – 12)
(x^2+4x-8)/(x-2)= (x+6) + 4/(x-2)
With synthetic division, you can try this notation:
2 ) 1 4 -8
1 6 4
(x^2+4x-8)/(x-2)= (x+6) + 4/(x-2)
It’s tough to solve an equation in this format. That being said, I initially like using the synthetic version if the equation is in the right format. If it is being divided by a variable with a degree of one, the process of dividing is simplified in the way the equation looks. Below it is apparent just from looking that I was able to more cleanly layout the problem using synthetic by using a table because it is a more organized and efficient way to go about it.
The process of synthetic is taking the coefficients of the numerator and using the constant in the denominator. Any coefficients in the numerator that are skipped (2x^5+3X^2) must be represented by zeros. Other than that, its as simple as multiplying and adding. Another important step is to negate the constant of the denominator before going through the process.
Long division is very reliable and I also don’t mind doing it this way. As a matter of fact, when I did the same problem using long division I found an error I made in the synthetic solution. It is proven and is much more capable when denominators do not have variables with a degree of 1.
|-2||+||-16 +||20 +||-32|
x +2 ) 8 x^3 + 6x^2 – 4x + 12
-(8x^3 + 16x^2)
0 +16x +12
– -16x + 32
-20 = Remainder
Why Synthetic Division Works (2012). Retrieved from https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-synthetic-division-of-polynomials/v/why-synthetic-division-works (Links to an external site.)
Bittinger, M. L., Beecher, J. A., Ellengoben, D. J., and Penna, J. (2016). Algebra & trigonometry: Graphs and models (6th ed.). [E-reader version]. Upper Saddle River, NJ: Pearson. Retrieved from http://www.pearsonmylabandmastering.com/northameri…
Good evening class,
For this post, I decided to write the equation of (x^2 + 6x – 2) / (x + 3).
For long division:
1 + 3
x + 3 ) x^2 + 6x – 2
– x^2 + 3x
3x – 2
– 3x + 9
So the answer is x + 3 -(11 / (x + 3))
For synthetic division:
-3 | 1 6 – 2
| – 3 – 9
1 3 -11
And the answer is still x + 3 -(11 / (x + 3)) or I have completed both of these calculations completely wrong, but either way, this is the answer I’m providing.
Overall, I found the long division method to be easier. While I can see the usefulness of the synthetic division, I find it easier for me to mess up. I would need to practice doing it more, but I think I’ll stick with the long division in the mean time.