Hello,
could you help me understand the procedure of finding the GCD of two polynomials step by step, using the Euclidean Algorithm?
For example
$\displaystyle a = x^3 - 3x +2 , b = x - 1$
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 $\displaystyle (x^3 - 3x + 2) = (x-1)(x^2 + x - 2)$ by long division.
Thus, $\displaystyle \gcd = x-1$
When using the Euclidean algorithm you repeating apply the division algorithm in several steps until you get rid of the remainder. The problem here is that first application already produces no remainder. That is why this is not a good example.
Look at this.Should they be polynomials of higher degree?
It has examples for both numbers and polynomials.
Both are extremely cases similar.