"Biotic factor" is a phrase because it does not contain a verb. A phrase is a word or a set of words that is found in a sentence and cannot stand alone. You may be tempted to list "biotic factor" as a clause, but this use would be grammatically incorrect. A clause always contains a verb. Thus, "biotic factor" must be a phrase and must be a dependent part of a sentence.
Biology Online defines the word "biotic" as "of, pertaining to, or produced by life or living organisms." By carefully studying this definition, it becomes obvious that "biotic" is an adjective. An adjective is a word that is used to describe or modify a noun. When trying to determine the part of speech of the entire phrase "biotic factor," realize that "biotic" is in fact an adjective and not a verb.
The word "factor" can be used as a noun or a verb. For example, in mathematics, when you factor an equation, you solve an equation to find the factors of that equation. However, when studying the definition of "biotic factor," it becomes evident that the "factor" in the phrase is not a verb, but a noun. A noun is a word that is used to name a person, place or thing.
After developing a clear understanding of the definition of "biotic factor," as well as the parts of speech of the individual words in the phrase, it becomes obvious that "biotic factor" can be defined specifically as a noun phrase. A noun phrase is made up of a noun and its modifiers. Remember, a noun phrase will not have a verb. In this case, "factor" is the noun and "biotic" is the noun's modifier, making this phrase a noun phrase.