1. GCD of polynomials

Hello,
could you help me understand the procedure of finding the GCD of two polynomials step by step, using the Euclidean Algorithm?
For example
$a = x^3 - 3x +2 , b = x - 1$
Thanks.

2. Originally Posted by drthea
Hello,
could you help me understand the procedure of finding the GCD of two polynomials step by step, using the Euclidean Algorithm?
For example
$a = x^3 - 3x +2 , b = x - 1$
Thanks.
There is no need to use Euclidean here and besides it does not work since it produces the answer in the first line.
Therefore, it does not give any infromation in this problem.

Just note $(x^3 - 3x + 2) = (x-1)(x^2 + x - 2)$ by long division.
Thus, $\gcd = x-1$

Could you give me an example of where the Euclid's algorithm can be used,
concerning polynomials? Should they be polynomials of higher degree?

4. Originally Posted by drthea