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I believe you are referring to FaceBook notifications. These can be controlled, as can ANY notification, fairly easily. Go to Settings from your homescreen, then Notifications, then scroll down to the App who's notifications you want to adjust, in this case FaceBook, click on it, and you will see, several toggles, along with a short explanation. You may want to set Allow Notifications to (Off, or not green), OR just turn off the sound, or Show options, etc.
Try and see what you like. You can control ANY app's notifications this same way.