An infinitive is a verb that is used as a noun, an adjective, or an adverb. Usually it is the simple verb form preceded by the word “to.” In the sentence: “Karen and Donna need to eat the bran muffins quickly,” “to eat” is the infinitive and is operating like a noun, a direct object to be specific, because it’s WHAT we need to do. Splitting the infinitive would be “Karen and Donna need to quickly eat the bran muffins.” No word, such as “quickly,” should come between the “to” and the simple verb, in this case “eat.” A better way to write this sentence would be, “Karen and Donna need to eat the bran muffins quickly.”
An infinitive can operate as an adjective. “When we go to the Duke reunion, William must bring a book to read so that he won’t get bored while Donna and Karen are eating bran muffins.” “To read” is our infinitive here, and it’s acting the part of an adjective by modifying “book.”
Here’s an infinitive that wants to be an adverb. “Richard cleaned his campus apartment bathroom to show us that he’s learned more at college than just economics.” “To show” is the infinitive, an adverb this time, explaining why Richard cleaned the bathroom—although it does nothing to tell us why it took 21 years for him to learn this skill.