Polymers formed in this way, where both ends of the growing chain have functional groups which can react with a monomer or with the appropriate functional group on another chain, are called step-growth polymers. Let's look at another step-growth polymer, but this time we'll look at the monomers and propose a structure for the polymer that would result.
The monomers are a dicarboxylic acid (terephthalic acid) and a dialcohol, also called a diol (ethylene glycol). We immediately recognize that these monomers can make an ester, so that we expect our polymer to be linked by ester functional groups. The resulting polymer is called polyethylene terephthalate and is the common polyester of plastic pop bottles and polyester fabrics.