Which service facilitates building and training deep learning models by providing pre-built algorithms?

Amazon SageMaker is the correct choice because it is specifically designed to facilitate the development, training, and deployment of machine learning models, including deep learning models. SageMaker provides a comprehensive environment that includes pre-built algorithms, frameworks, and tools, allowing developers to build and iterate on their models efficiently.

The pre-built algorithms in SageMaker cover a wide range of tasks, such as image classification, natural language processing, and more, which significantly speeds up the model building process. In addition, SageMaker also offers capabilities for scaling the training process on powerful computing resources, thus making it easier to work with large datasets and complex models.

The other services listed do not focus on building and training deep learning models. Amazon EC2 provides scalable computing capacity in the cloud but does not provide specialized tools for machine learning. Amazon RDS is a managed relational database service that is focused on data storage rather than model training. Amazon Textract is a service for extracting text and data from documents, which is useful for specific applications but does not facilitate the end-to-end machine learning process.