Highest common factor question

[Mike012]

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.

 

[spamiam]

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.

 

[eumyang]

Are you and Miike012 the same person? I remember seeing this exact problem before. I explained this HCF method here:
https://www.physicsforums.com/showthread.php?t=460815"

 

[bcrowell]

Closed as a duplicate of the other question.