We wre exceedingly pleased that Rex come home.. Is exceedingly an adjective?

No.

Check the dictionary entry. What part of speech does it say for this word?
http://www.answers.com/topic/exceedingly

No, it's an adverb because it is modifying the adjective please. :)

Yes, "exceedingly" is an adverb. Adverbs typically describe or modify verbs, adjectives, or other adverbs. In the sentence you provided, "exceedingly" is modifying the adjective "pleased," emphasizing the extent or intensity of the pleasure.

To determine if a word is an adjective or adverb, you can follow these steps:

1. Identify the word you want to determine the part of speech for.
2. Determine what the word is describing. If it is modifying a noun, it is likely an adjective. If it is modifying a verb, adjective, or adverb, it is likely an adverb.
3. Confirm if the word answers "how," "when," "where," "why," or "to what extent" with regard to the action or description being modified. If it does, it is likely an adverb.

By following these steps, you can analyze the sentence structure and parts of speech to identify the function of a particular word.