ISIS is really an ideology. It is a group of roque Islamic extremists who have decided to rule over others until they conform to their views. They are finding those with low self-esteem and no purpose in life and giving them a direction. The Iraqi army right now is taking one province back at a time but that's not enough. They can truly help eradicate ISIS through a comprehensive plan of law and order, jobs for disenfranchised youths, incorporate Sunnis and Shiite Muslims into the government at all levels. There also has to be education for all members of their society. It is a difficult task but it can be done.
The Iraqi army has little chance of defeating ISIS on their own. One of the primary reasons of course is that ISIS extends beyond Iraq. Even if the Iraqis were able to overthrow ISIS within Iraq, there is still a strong chance that they could make a comeback. A broader international collective effort will be needed to effectively eradicate ISIS and even that will be difficult to do.
The Iraqi Army may want to eradicate ISIS however they cannot do it on their own. ISIS is very well funded and has weapons they never should have gotten their hands on. The Iraqi Army on the other hand is underfunded and understaffed and faces some fellow countrymen that do not support them.
ISIS came out of Syria forcing its people to fight for Iraq - and the elimination of ISIS makes the Syrian government stronger. But I do not think that Iraq has the manpower to eradicate ISIS. Such is why they needed Syria's help in fighting the U.S. And ISIS is stronger than Iraq's army.