Let F be a field and let dX sX tX and mX be polynomials in F

Let F be a field and let d(X), s(X), t(X) and m(X) be polynomials in F[X] with m(X) of positive degree. Prove that if d(X) = gcd(t(X), m(X)) and d(X) divides s(X), then there is a polynomial

j(X)

Solution

ALL SYMBOLS USED ARE POLYNOMIALS DROPPING (X) AS UNDERSTOOD .. GIVEN D , S , T , M , ARE POLYNOMIALS IN X , WITH M BEING OF POSITIVE DEGREE