Bezout coefficients for Polynomials [closed]

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I want to find the bezout coefficient for those 2 polynomials :

f = 1+x-x^2-x^4+x^5 and g = -1+x^2+x^3-x^6 when I use the gcd function in sage the output is :

sage: gcd(f,g)
sage: 1

but when I use xgcd(f,g) it gives me the following :

(-27, 9x^5 - 18x^2 - 9x - 9, 9x^4 - 9x^3 - 18x + 18)

I want xgcd to give me 1 instead of -27 so the polynomials will be the bezout coefficients

P.S: I can't divide the polynomials by -27 because i'm working in ZZ