Homework help (Basic Algebra-Division of polynomials)

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Discussion Overview

The discussion revolves around the division of polynomials, specifically focusing on simplifying and performing long division and synthetic division. Participants are seeking help with specific polynomial expressions and the methods used to divide them.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents a polynomial division problem: \(\frac{4x^3 - 8x^2 + 5x +1}{x+2}\) and questions the understanding of long division of polynomials.
  • Another participant provides a different polynomial for division: \(\frac{5+5x-8x^2+4X^3-3x^4}{2-x}\) and shares their result, which includes a remainder.
  • A participant describes their approach using short division and expresses uncertainty about their method, specifically regarding the coefficients and the divisor.
  • Another participant mentions using synthetic division and provides a result that includes a polynomial expression and a fraction.
  • One participant points out a potential misunderstanding in the method being used and suggests a correction related to multiplying by the additive inverse of the divisor's coefficient.
  • Another participant shares their own result from the division process, which appears to be a variation of the previous results.

Areas of Agreement / Disagreement

The discussion includes multiple competing views and methods for polynomial division, with no consensus reached on the correct approach or final results. Participants express uncertainty and seek clarification on their methods.

Contextual Notes

Participants' methods and results vary, and there are indications of confusion regarding the application of synthetic division and the handling of coefficients. Some steps in the division processes remain unresolved or unclear.

Krazie
Please go to the bottom of this page for the problem that I am having trouble with.
 
Last edited by a moderator:
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Simplify the numerator

[tex]\frac{4x^3 - 8x^2 + 5x +1}{x+2}[/tex]

Now, do you know how to do long division here? Or in general rather, long division of polynomials? I would hope you do, otherwise I don't understand how they can ask this question of you. If you do, then the problem should be easy. If you don't know, I don't know why they'd ask it, and it might be kind of hard to explain it here, as it would be hard to give examples (I don't know if there is latex code that can be used).
 
Uhh... I see you've edited it. What does this new thing have to do with polynomials or algebra? What is the problem now?
 
I am going to try it again. Here is the problem:
[tex]\frac{5+5x-8x^2+4X^3-3x^4}{2-x}[/tex]
 
I am coming up with :
[tex]-3^3 +4x^2 -8x+5[/tex] with a remainder of 117
 
I am using short division. I am using only the coeficients in the dividend ordered from highest degree exponent to lowest, divided by the additive inverse of the divisors coeficient. First thing that I do is drop the -3, then multiply the -3 by the divisors coeficient, which is -2. I think that I am doing something wrong there. Can anyone help me?
 
Using synthetic div I got

[tex]\frac{-33}{2-x}+(19 + 12 x + 2 x^2 + 3 x^3)[/tex]

I think you're using the same method. If so, you should multiply by 2. Remember that when dividing by x-c you multiply by c.
 
Last edited:
i came up with - (3x^3 + 2x^2 + 12x + 19) - 33 / 2 - x
 

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