What Generates the Ideal in Q[X] with Polynomials x^2+1 and x^6+x^3+x+1?

[iNCREDiBLE]

Consider the ideal $$I$$ of $$Q[x]$$ generated by the two polynomials $$f = x^2+1$$ and $$g=x^6+x^3+x+1$$

a) find $$h$$ in $$Q[x]$$ such that $$I=<h>$$
b) find two polynomials $$s, t$$ in $$Q[x]$$ such that $$h=sf+tg$$

 

[Euclid]

Have you even given this problem a shot? It's fairly easy.
Consider the ideal I of Z generated by 12 and 20. Do you know how to find a single number x that generates I? If you can't do this, you won't be able to do this problem either.