Proper is an adjective, factor is a noun.
Each word in the phrase belongs to some part of speech. "Daedalus" and "Icarus" are proper nouns. "Son" is a common noun. "And" is a conjunction. "Is" is a verb.
A phrase is never a part of speech, only a word.
Prepositional phrase
"last" is an adjective, and Saturday is a proper noun (always capitalized).
The phrase "in addition" is a prepositional phrase in which "in" is the preposition and "addition" is its object. This phrase, as a phrase, is not a part of speech, although it may function as one, probably an adjective or adverb.
A prepositional phrase.
Proper is an adjective.
On the mountain top is a preposition phrase, not a part of speech.
Truman is a name, so therefore as a part of speech it is a proper noun.
That I am is a phrase, the individual words in the phrase are parts of speech. That -- demonstrative, determiner I -- pronoun am -- be verb
adverb phrase
verb