$R$ is a commutative ring and $M$ is a maximal ideal of $R$. It is stated (without proof) in my text that the polynomial ring $(R/M)[X]$ is isomorphic to $R[X]/M[X]$, but I cannot see why this is the case.
I tried to work explicitly from the definitions, looking at cosets of the RHS and comparing them to elements from the LHS, but did not have any luck. I also thought of appealing to the three Isomorphism theorems, but could not see how to apply them to this problem.
Please advise as to how I would go about finding an isomorphism between these two structures, or another method I could use to make better understand this correspondence. Thank you.