Step 1: Identify the repeating unit of a nucleic acid.
DNA and RNA are long chains built by linking together small repeating units, and each such unit is called a nucleotide, made of a nitrogenous base, a pentose sugar, and a phosphate group all joined together.
Step 2: See how these units are strung together.
Neighbouring nucleotides are joined through phosphodiester bonds running between the $3'$ carbon of one sugar and the $5'$ carbon of the next, building up the long sugar phosphate backbone.
Step 3: Rule out the other choices.
Amino acids build proteins, not nucleic acids; a nucleoside is only a sugar joined to a base, missing the phosphate that lets it link into a chain; and a pentose sugar is just one small piece of the full nucleotide, not the repeating unit itself.
Step 4: State the answer.
Since the chain repeats nucleotide after nucleotide, nucleic acids are polymers of nucleotides. \[ \boxed{\text{nucleotides}} \]