Question: Greatest common divisor

I'm trying to find the greatest common divisor of two functions with characteristic=7:

with(Algebraic):
GreatestCommonDivisor(x^4+x^3+4*x^2+4*x+5,x^3+x^2+5*x+5,'characteristic'=7);

This gives the answer as (x+4) which is a common divisor but it is not the greatest. From working by hand, I've found that (3x+5) is the gcd.

Why is maple giving the wrong answer?

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