# Polynomial function/R/Degree d/(d+1)-te Derivative/Exercise

Prove that a polynomial ${\displaystyle {}P\in \mathbb {R} [X]}$ has degree ${\displaystyle {}\leq d}$ (or it is
${\displaystyle {}P=0}$), if and only if the ${\displaystyle {}(d+1)}$-th derivative of ${\displaystyle {}P}$ is the zero poynomial.