abstract algebra - How do I find the order of an element if I am given the minimal polynomial of the element?

For example, let's say I am given an element $α$ in a field of characteristic $2$. Further, I am given the minimal polynomial of α with respect to $GF(2)$. Let's say that minimal polynomial is $f(x) = x^9 + x + 1$. How would I then deduce the order of $α$?

This is for a coding theory assignment, but I cannot deduce from the literature how to go in this direction. Most things I have read seem to indicate how to find a minimal polynomial, but don't seem to take that any further.