Factorise p(x) as a product of linear factors

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Homework Help Overview

The discussion revolves around the factorization of a polynomial into linear factors, with participants exploring methods and reasoning related to polynomial roots and factorization techniques.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the rational root theorem and its implications for identifying possible rational roots of the polynomial. There are mentions of using synthetic division after finding a root, as well as considerations about the clarity and presentation of mathematical work.

Discussion Status

Some guidance has been provided regarding the use of the rational root theorem and synthetic division. Participants are engaged in reviewing each other's work and suggesting improvements, indicating an ongoing exploration of the topic without a clear consensus on the best approach yet.

Contextual Notes

There are concerns about the legibility of submitted work, which may affect the clarity of the discussion. Participants are also reflecting on the balance between guesswork and systematic reasoning in their approaches to solving the problem.

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Last edited by a moderator:
jbunniii said:
Can you start by stating the rational root theorem, and what it says about the possible rational roots of the polynomial?

ok! i will try that. :smile:
 
After you find one root, I would use synthetic division to find the others.

But I guess it this case you really don't have to.
 
Last edited by a moderator:
The scan of your work is illegible. It appears that you did your work on graph paper, and possibly in pencil, making what you wrote very difficult to read.
 
hostergaard said:
Here is it finished, could somebody prof-read it and comment? tell if there's some improvements to be done. ;-)
http://img33.imageshack.us/img33/72/opgave3.th.jpg

Guesswork is a good thing in mathematics, but guesswork often need some kind of reasoning. Drawing a graph by hand / on computer is not guesswork in this case. You should come up with a more sophisticated way of showing what your guesswork builds on.

One way to go by, is to look at the last number in the polynom, and factorize that number, finding numbers that constitute 56. You would then get some of the roots you have come up with doing your "guesswork". After that, do polynom division. Or two.
 
Last edited by a moderator:

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