Final answer:
The correct option is c. Hashing.
The most efficient and scalable search method that uses a product search index is hashing. Hashing drastically reduces the time needed to find an item by using a hash code to index directly into a table.
Step-by-step explanation:
The method that is efficient and scalable because it uses the product search index rather than searching through each item linearly is hashing. Hashing involves converting the key associated with a piece of data into a hash code, which then determines the index at which the data is stored in a table.
This allows for quick retrieval of data, as the hash code directly leads to the index where the data can be found, bypassing the need for sequential searching. On the other hand, binary search is efficient on ordered lists but still requires comparison checks, linear search is slow and not scalable for large datasets, and search engine optimization is a process for improving the visibility of a website or a web page in a search engine's unpaid results, rather than a search method in data structures or databases.