How find gcd polynomials? How to find gcd of polynomials $gcd(x^3+x^2-x-1,3x^2+2x-1)$ ??
I divide of polynomials. It worked like this $\frac 13 x - \frac19$,$ R\left( x\right) =-\frac89x -\frac89$

You want the gcd of $f(x) = x^3+x^2-x-1$ and its derivative. Now 
$$f(x) = x^2 (x+1) - (x+1) = (x^2-1)(x+1) = (x-1)(x+1)^2$$ so 
$$\gcd(f(x), f'(x)) = x+1$$
