An http://www.answers.com/topic/infinitive is the "to" form of a http://www.answers.com/topic/verb, as in "to play." A split infinitive is a http://www.answers.com/topic/phrase in which to is separated from the verb. The sentence "I decided to quickly and directly go home" contains a split infinitive. Some people consider it poor style, or even incorrect style, to split an infinitive. I prefer to think of split infinitives as generally unnecessary. Given a little thought, one can usually construct a better sentence. The sentence "I decided to go quickly and directly home", is more easily understood.