So here is the exact question that i am having trouble on:
"Extend the Euclidean algorithm to polynomials and find the greatest common divisor of:
$3x^5-10x^4-4x^3-14x^2-7x-4$
and
$3x^4+11x^3-5x^2-5x-4$"
Now, i know how to find the gcd using Euclidean's algorithm for all integers as well as polynomials but i am having trouble with this one... I tried wolfram alpha at first and it gave me the gcd of: $3x^2+2x+1$. Then i did it by hand and i keep getting a completely different gcd: $\displaystyle \frac{612}{169}x^2+\frac{408}{169}x+\frac{204}{169}$.
Here is my work for how i used Euclidean's algorithm:
Can someone tell me what i am doing wrong [and why] and which one is the correct answer? Thanks!