Let $R$ be a graded ring and $M$ a graded $R$-module. An element $x\in R_{l}$ is said to be superficial for $M$ if $(0:_{M} x)_{n}=0$ for all but finitely many $n$.
Let $M$ be a finite generated $R$-module of positive dimension and $x\in R_{+}$ a superficial element for $M$. If $\dim(M)>1$ prove that $e(M/xM)=\deg(x)e(M)$, where $e(M)$ is the first coefficient of Hilbert polynomial.