GCD Euclidean algorithm x WolframAlpha

Question

I was given the following exercise:

Find the gcd of $x^4+x^3+2x^2+x+1 $ and $x^3+4x^2+4x+3 $ in $\mathbb{Q}[x]$ using the Euclidean algorithm.

Well, I used the Euclidean algorithm and got $10x^2+10x+10$. But then I decided to check it on WolframAlpha and got $x^2+x+1$,that is the same answer divided by 10.

Also,by factorization of the polynomials I got the same answer as WolframAlpha.

I think that I can “ditch” the 10 on the answer I got using the algorithm but I don’t see why (maybe I am overlooking some propriety of the gcd?)

score 2 · Accepted Answer · answered Sep 09 '19 at 17:06

2

Both answers are correct. Note that $10$ is a unit in $\mathbb Q$ and so the two answers are associates.

answered Sep 09 '19 at 17:06

lhf

221,500

Please strive to organize vs. creating more dupes for FAQs. – Bill Dubuque Sep 09 '19 at 17:55
@BillDubuque, you're quite right. Thanks for finding those duplicates. – lhf Sep 09 '19 at 18:56

GCD Euclidean algorithm x WolframAlpha

1 Answers1