Need help for this algebra problem Show that fx divides a po

Need help for this algebra problem:

Show that f(x) divides a power of m(x). m(x) is the minimal polynomial, and f(x) the characteristic polynomial in terms of the elementary divisors of A.

Solution

By division f(x)= a(x)m(x)+r(x)

where the degree of r(X)

Is less than that of m(x) since m(x) =0

since the degree of r(x) < that of m(x) we must have that r(x) identically zero.