As mentioned in the title:
f(x) and g(x) are polynomials above the Rationals field. if $ f^2(x)=g^2(x)(x^2+1) $ then does it mean that $ gcd( f^2(x),g^2(x))=(x^2+1) $? or maybe it isn't the greatest common divisor but some divisor that was found.
By Euclid's algorithm it seems that's exactly the gcd, but it seems logical to me that maybe it's some divisor as well.. please help? Thanks