Length of module $\otimes A[X]$

Question

Let $M$ be an $A$-module of finite length, i.e. $\ell_A(M)<+\infty$. I would like to compute the length $$(*) \: \: \: \ell_{A[X]}(M\otimes_AA[X]),$$ where $A[X]$ is the canonical polynomial ring on $A$. As it has been pointed out in the comments we have to assume that ($*$) is finite. I think that ($*$) is equal to $\ell_A(M)$, but I do not know how to proceed. Any help?