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:**

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) ——————- 4 <----------------remainder

(x^2+4x-8)/(x-2)= (x+6) + 4/(x-2)

With synthetic division, you can try this notation:

2 ) 1 4 -8 2 12 ——————- 1 6 4(x^2+4x-8)/(x-2)= (x+6) + 4/(x-2)POST1:It’s tough to solve an equation in this format. That being said, Iinitially like using the synthetic version if the equation is in theright 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 cleanlylayout the problem using synthetic by using a table because it is a moreorganized and efficient way to go about it.The process of synthetic is taking the coefficients of the numeratorand using the constant in the denominator. Any coefficients in thenumerator that are skipped (2x^5+3X^2) must be represented by zeros.Other than that, its as simple as multiplying and adding. Anotherimportant step is to negate the constant of the denominator before goingthrough the process.Long division is very reliable and I also don’t mind doing it thisway. As a matter of fact, when I did the same problem using longdivision I found an error I made in the synthetic solution. It is provenand is much more capable when denominators do not have variables with adegree of 1.

Synthetic Division:

(8×3+6×2−4x+12)x+286

-412

-2↓ +

– 16+ 20 + -32

8

-1016

-20RemainderAnswer= 8×2−10x+16−20x+2

Long Division:

______ 8x^2_-10x_+16_________x +2 ) 8 x^3 + 6x^2 – 4x + 12 -(8x^3 + 16x^2) ————————————– 0 -10x^2

-10X^2 -20x

————————————————

0 +16x +12

– -16x + 32

——————————————————–

-20 = Remainder

Answer= 8×2−10x+16−20x+2

References:

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*(6thed.). [E-reader version]. Upper Saddle River, NJ: Pearson. Retrievedfrom

http://www.pearsonmylabandmastering.com/northameri…

POST2:

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

– 11

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 completedboth of these calculations completely wrong, but either way, this is theanswer I’m providing.Overall, I found the long division method to be easier. While I cansee the usefulness of the synthetic division, I find it easier for me tomess up. I would need to practice doing it more, but I think I’llstick with the long division in the mean time.