Synthetic division (small part of a bigger problem)

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Homework Help Overview

The discussion revolves around the process of synthetic division applied to the polynomial expression (x^3-2)/(x^2+11x+24). Participants are examining the simplification and proper representation of the quotient and remainder in polynomial division.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore the validity of the remainder obtained after the initial division and question the presence of a quadratic term in the remainder. There are suggestions to perform synthetic division again with the remainder, and some participants express confusion about the proper form of the quotient and remainder.

Discussion Status

The discussion is active, with participants questioning the correctness of the initial division and the nature of synthetic division. Some guidance has been offered regarding the proper format of the quotient and remainder, but there is no explicit consensus on the next steps or resolution of the problem.

Contextual Notes

There is a mention of the need for clarity on the polynomial division process and the specific conditions under which synthetic division is applicable. Participants note the absence of detailed work from the original poster, which complicates the discussion.

graycolor
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(x^3-2)/(x^2+11x+24) can't seem to simplify this I get x+(-11x^2-24x-2)/(x^2+11x+24) that doesn't seem right.
 
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It's right but why do you still have a quadratic term in the numerator and denominator of the remainder? That's not really a proper remainder, is it? Don't you want x-11+remainder?
 
I've thought about doing synthetic division again with the remainder... would that be right. If I did I would get -11 that would cross out with my +11 and add a remainder.
 
graycolor said:
I've thought about doing synthetic division again with the remainder... would that be right. If I did I would get -11 that would cross out with my +11 and add a remainder.

"Cross out with +11"? What +11? Yes, the quotient should be x-11 and the remainder a linear polynomial over x^2+11x+24.
 
First of all, you aren't doing "synthetic division". Synthetic division is used to divide a polynomial by a first order term of the form x- a only. What you are doing is just division with polynomials.

It's hard to comment since you didn't show your work. Did you handle the "0x2" and "0x" in the dividend properly?
 

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