Polynomial Division: Simplifying with Long Division

In summary, the conversation is discussing a polynomial division problem and seeking help. The original poster provides the equation and asks for assistance, while another user asks for clarification and suggests checking the basics of polynomial division. The conversation ends with the suggestion to show work and potentially find an easier method for simplifying the problem.
  • #1
chris92
2
0
1. Hi I have a question I am stuck on it is:

(x3 + 2x2y - 2xy2 - y3)/(x-y)

Can anyone help?



Homework Equations





The Attempt at a Solution


 
Last edited:
Physics news on Phys.org
  • #2
What do you mean by "help"? What help do you need or want? You title this "long hand polynomial division" (I would have said just "polynomial division"- "long hand" makes me think of cursive writing!) so apparently you know what you are supposed to do. How many times does x divide into [itex]x^3[/itex]? What do you do next?
 
  • #3
chris92 said:
1. Hi I have a question I am stuck on it is:
x3+2x2y-2xy2-y3/x - y

Can anyone help?



Homework Equations





The Attempt at a Solution


What you have written is not a polynomial; it is a rational function of the form
[tex] x^3 + 2 x^2 y -2xy^2 - \frac{y^3}{x}-y.[/tex] Did you intend to write
[tex] \frac{x^3 + 2x^2y-2xy^2-y^3}{x-y} ?[/tex]
If that is what you meant you should have used parentheses, like this:
(x3 + 2x2y - 2xy2 - y3)/(x-y).
 
  • #4
Hi yes that is what I meant sorry .
 
  • #5

there is more in wikipedia too. Since this is a simple example i think you should check the basics of polynomial division. It's nothing too difficult, it simply requires a little practice.
 
Last edited by a moderator:
  • #6
@chris92 -- check your PMs, and then show your work on your problem here in this thread.
 
  • #7
@chris92: Are you required to do long division? There is a much easier way to simplify it.

Edit: Woops, maybe not. I had a sign wrong...
 

FAQ: Polynomial Division: Simplifying with Long Division

What is long hand polynomial division?

Long hand polynomial division is a method for dividing two polynomials with multiple terms using long division. This method involves writing out the polynomials in a specific format and performing division operations to find the quotient and remainder.

What are the steps for performing long hand polynomial division?

The steps for long hand polynomial division are as follows:

  1. Arrange the polynomial being divided (dividend) and the polynomial dividing (divisor) in descending order of degree.
  2. Check the leading term of the dividend and the divisor.
  3. If the degree of the leading term of the dividend is less than the degree of the leading term of the divisor, the division is not possible.
  4. Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient.
  5. Multiply the first term of the quotient by the divisor and subtract it from the dividend.
  6. Bring down the next term of the dividend to the remainder.
  7. Repeat the process until all the terms of the dividend have been used.
  8. The final result will be the quotient and remainder.

What is the purpose of using long hand polynomial division?

The purpose of using long hand polynomial division is to simplify complex polynomial expressions and to find unknown coefficients or roots of a polynomial equation.

What are some common mistakes to avoid when performing long hand polynomial division?

Some common mistakes to avoid when performing long hand polynomial division include:

  • Forgetting to bring down the next term of the dividend to the remainder.
  • Incorrectly dividing the leading term of the dividend by the leading term of the divisor.
  • Not subtracting the product of the first term of the quotient and the divisor from the dividend.
  • Incorrectly writing the final result as the quotient and remainder.

Are there any alternative methods to long hand polynomial division?

Yes, there are alternative methods to long hand polynomial division, such as synthetic division, which is a shorter and faster method for dividing polynomials. However, long hand polynomial division is still widely used and is important for understanding the concept of polynomial division.

Similar threads

Showing a polynomial is divisible by another over Z_5
Replies
3
Views
2K
Constructing a splitting field for polynomial over F_5
Replies
5
Views
2K
How to check if a polynomial is irreducible over the rationals
Replies
18
Views
3K
Showing that one polynomial divides another
Replies
8
Views
1K
Find limit for rational function
Replies
14
Views
2K
Abstract algebra Polynomials and Prime
Replies
3
Views
1K
Laurent series by long division of trig function
Replies
15
Views
3K
Solving quartic equations using synthetic division
Replies
18
Views
4K
Derivative of a Fraction: Simplifying with Polynomial Division?
Replies
10
Views
2K
Base 8 Logic Puzzle: Finding Solutions to Divisibility Rules
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top