Model Bézier curve of N control points with more Bézier curve of n-1 points.

Question

Given a Bézier curve defined by N control points. Is it possible to model that curve using a finite amount of Bézier points with less than N control points?

eg. Model a 4 control point Bézier with 2, 3 control points Bézier.

Answer 1

Got it. Take your first Bezier curve. Select all the control points except the last and make one curve out of that. Then another curve out of every point but the first and that's your second curve.

Answer 2

In general, you cannot exactly model a Bezier curve of $N$ control points by multiple lower-degree Bezier curves unless this Bezier curve is degree-elevated from lower degree Bezier curve.