Final answer:
RNA polymerase II is the eukaryotic enzyme responsible for transcribing nearly all protein-coding genes into pre-mRNA, which is then processed to form mature mRNA.
Step-by-step explanation:
The eukaryotic RNA polymerase responsible for transcribing nearly all protein-coding genes is RNA polymerase II. In eukaryotes, three RNA polymerases have distinct roles related to different types of RNA. While RNA polymerase I is involved in synthesizing rRNA and RNA polymerase III is responsible for transcribing tRNA and small RNA genes, it is RNA polymerase II that specializes in synthesizing all protein-coding nuclear pre-mRNAs. The pre-mRNA then goes through extensive processing to become mature mRNA, which can then be translated into proteins. The synthesis by RNA polymerase II takes place in the nucleus of eukaryotic cells and is crucial for gene expression.