The polynomials $B_m$ are defined by $$\forall m \in \mathbb{N}, \quad B_m(x) = \sum_{k=0}^m \binom{m}{k} b_k x^{m-k}.$$ Show that, for all integer $m \geqslant 2$, $B_m(1) = b_m$, then that, for all integer $m \geqslant 1$, $B_m' = m B_{m-1}$.
The polynomials $B_m$ are defined by
$$\forall m \in \mathbb{N}, \quad B_m(x) = \sum_{k=0}^m \binom{m}{k} b_k x^{m-k}.$$
Show that, for all integer $m \geqslant 2$, $B_m(1) = b_m$, then that, for all integer $m \geqslant 1$, $B_m' = m B_{m-1}$.