Defining a curve as a Bezier curve

A Bezier curve is significant with its control points. When control points are given, the Bezier curve can be written using De Casteljau's algorithm. An important property of Bezier curve is that every coordinate function is a polynomial. Suppose that a curve $ \alpha (t) $ is a curve which coordinate functions are polynomial. Can we find points that make the curve $ \alpha (t) $ as Bezier curve? This article presents a method for finding points which present $ \alpha (t) $ as a Bezier curve