That will take up an awful lot of disc space if I kept the backups.
Well, for example, I use Macrium Reflect free edition. Each image created is actually compressed, so you usually can have multiple images saved going back in time. If your backup drive starts to get low on space, just delete the oldest image, or you can have MR do it automatically. The first time you use MR, it will prompt you to create an emergency restore disk so be sure and do that. In addition, each image is searchable, so you can actually boot an image and retrieve any data you have on it at the time you made it. That's really a handy feature.
I have my backup drive on a docking station which is connected via USB cable (it comes with the docking station) to my computer and sits on my desk. I can pop my backup drive (or any other drive) in and out without rebooting the computer. I see that your computer is a laptop so that would be the best way to go. This is a system that you will always use even if you get a new computer down the road.
Re: "factory reset"; that is not the correct term, but I suspect that you are referring to the same thing as a "Restore Partition". This is a separate, hidden partition on your laptop's drive that contains the original image of your operating system, and that image can be accessed by pressing certain key(s) on boot, usually one of the F keys. This way, you can reinstall your complete OS (operating system) and restore your computer back to when it was first purchased. That would take care of any corrupted system files including your restore problems. However, be aware that in so doing, you will loose any and all data, installed programs, browser shortcuts, emails (if you are using a local client email program such as Outlook) on your computer.So it would be necessary to pull anything you want off the computer first and save to a HD, flash drive or burn to DVDs, and make sure that you have the installation files for any programs you added.
Note....if, in the past, you wiped your entire HDD for any reason, that restore partition may be gone, in which case the above will not apply.