Factorise p(x) as a product of linear factors

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SUMMARY

The discussion focuses on the factorization of a polynomial p(x) into linear factors using the Rational Root Theorem and synthetic division. Participants emphasize the importance of presenting mathematical work clearly, noting that the original submission was difficult to read. They suggest starting with the Rational Root Theorem to identify possible rational roots and recommend using synthetic division to simplify the polynomial further. Additionally, they highlight the need for a structured approach to factorization, including analyzing the constant term of the polynomial.

PREREQUISITES
  • Understanding of the Rational Root Theorem
  • Familiarity with synthetic division
  • Basic polynomial factorization techniques
  • Ability to graph polynomials for visual analysis
NEXT STEPS
  • Study the application of the Rational Root Theorem in polynomial equations
  • Practice synthetic division with various polynomial examples
  • Learn advanced polynomial factorization methods
  • Explore graphing techniques for polynomial functions to identify roots visually
USEFUL FOR

Students studying algebra, mathematics educators, and anyone looking to improve their skills in polynomial factorization and mathematical presentation.

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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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