I got a bit stuck with finding the gcd for [MATH]x^5+x^3+x^2+x+2[/MATH] and [MATH]x^4+x^2+1[/MATH].
I started with the Eucledian algorithm and got that
[MATH]x^5+x^3+x^2+x+2 = (x^4+x^2+1)\cdot x+(x^2+2)[/MATH][MATH]x^4+x^2+1=(x^2+2)\cdot (x^2-1)+3[/MATH]But then got stuck..
Should the next step be [MATH]x^2+2=3\cdot \frac{2}{3}+ x^2[/MATH] or how do proceed?
I started with the Eucledian algorithm and got that
[MATH]x^5+x^3+x^2+x+2 = (x^4+x^2+1)\cdot x+(x^2+2)[/MATH][MATH]x^4+x^2+1=(x^2+2)\cdot (x^2-1)+3[/MATH]But then got stuck..
Should the next step be [MATH]x^2+2=3\cdot \frac{2}{3}+ x^2[/MATH] or how do proceed?