For joining pieces of recombinant DNA together, the enzyme typically used is ligase, not polymerase. Ligase is responsible for catalyzing the formation of phosphodiester bonds between adjacent nucleotides in DNA strands. This enzyme plays a crucial role in sealing nicks or gaps in the sugar-phosphate backbone of DNA molecules, effectively joining DNA fragments together into a continuous strand. Polymerase, on the other hand, is primarily involved in DNA replication and amplification processes such as PCR, where it synthesizes new DNA strands by adding nucleotides to a template DNA strand. While polymerase can extend DNA strands, it does not have the capability to join separate DNA fragments together in the same way as ligase.