Highest common factor question

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Homework Help Overview

The original poster seeks to determine the highest common factor (HCF) of two polynomials: 4x^3 - 3x^2 - 24x - 9 and 8x^3 - 2x^2 - 53x - 39. They question the effectiveness of a technique they encountered in an older book and inquire about alternative methods.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants discuss the potential use of the Euclidean algorithm for finding the HCF, while others mention factoring as an alternative for lower degree polynomials. The original poster questions the validity of the technique they read about and seeks opinions on its usefulness.

Discussion Status

The discussion includes various perspectives on methods for finding the HCF of polynomials. While some guidance on the Euclidean algorithm is provided, there is no explicit consensus on the best approach, and the original poster's concerns about the technique remain open for further exploration.

Contextual Notes

One participant notes a potential duplication of the question, referencing a previous discussion on the same problem, which may indicate a lack of new insights or clarity in the current thread.

Mike012
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I was reading an older book on how to find the HCF and I wanted to know if it is a good technique or just a waste of time?

Find the highest common factor of 4x^3 - 3x^2 - 24x - 9 and 8x^3 - 2x^2 - 53x - 39

Is anyone familiar with the method? Are there better methods out there?

Thank you.
 

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This looks like the Euclidean algorithm (http://en.wikipedia.org/wiki/Greatest_common_divisor_of_two_polynomials). If so, yes it's a very good way to find the highest common factor (also known as the greatest common divisor). If the polynomials are of small enough degree, you could alternatively try to factor them and then compare their factorizations. But I think the Euclidean algorithm is better for higher degree polynomials.
 
Closed as a duplicate of the other question.
 

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