Polymerization and the break down of a polymer are two opposite reactions. What role does a water molecule play in both of them?

Polymerization is a Chemical reaction in which two or more small, similar molecules are combined to make larger molecule

water molecule play in both of them because In polymerization (dehydration sysnthesis), a water molecule is removed when it is removed then bonds join monomers together.

In hydrolysis bonds between monomers are broken and a water molecule is inserted (as OH - and H+).