<s>[INST] What is $\gcd (x^{3}+6x^{2}+11x+6,x^{3}+1)$ When applying straight-forward Euclid's algorithm the result have fractional coefficients, but by factoring linear terms you get $x+1$. Which answer is right?
 [/INST] $(x^3+6x^2+11x+6,x^3+1)=((x+1)(x^2-x+1),(x+1)(x+2)(x+3)) = (x+1)((x^2-x+1),(x+2)(x+3)) = (x+1)$
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