Final answer:
The helix-turn-helix motif is a functional domain found in both eukaryotic transcription factors and bacteria, unlike other motifs such as the basic leucine zipper and zinc finger, which are typically found in eukaryotes.
Step-by-step explanation:
The eukaryotic transcription factors and bacteria share the helix-turn-helix motif as a functional domain found in both types of organisms. Transcription factors are proteins that bind to specific DNA sequences to regulate the transcription of genetic information from DNA to messenger RNA. In bacteria, the helix-turn-helix motif is a common structural motif capable of binding DNA, and it is also seen in some eukaryotic transcription factors. While other motifs like the basic leucine zipper and zinc finger are commonly found in eukaryotic transcription factors, the helix-turn-helix is the motif which is shared with bacterial proteins.