answered 3 years ago
One'd need to employ CRT here - for example:
R.<x> = PolynomialRing(QQ) print( crt([2*x-5,-5*x-9],[x^2-4,x^2+x+3]) )
gives x^3 + x^2 - 2*x - 9.
x^3 + x^2 - 2*x - 9