I believe you are experiencing 1 of 2 possibilities:
Was it slow before 8.1? If not...
Possibility #1 - Most Likely:
You are experiencing unexplainable Windows errors because of bugs in Microsoft's software. 8.1 is the latest OS that Microsoft offers. As a general rule of thumb, Microsoft's latest product is historically buggy during it's first 1-2 years of existence. Nobody is going to give you a good answer - because nobody can. Seriously. It's truth we all have to accept.
Here's what's happened (Please correct me where I'm wrong): You originally had Windows 8 on the Samsung laptop. The laptop came preloaded with Samsung's software for Windows 8. Recently the laptop has been 'successfully' upgraded to 8.1, but it is running slowly.
Your problem is a conflict between Samsung software and Windows 8.1.
Here's how I would make your laptop run like a champ (Please let me know if you need more details):
1. Backup all data
2. Format Hard Drive
3. Install Windows 8 with clean DVD (Not a Samsung DVD, nor "Factory Reset").
4. Install Windows 8 drivers for your Samsung model.
5. Update to Windows 8.1 (You might need to download 1 Windows update to get 8.1 to show up in Store. The update number ends with KBxxxxx389)
6. Install Windows 8.1 drivers for your Samsung model.
7. Fully update Windows 8.1
8. Check the Windows Defender is activated, or install the antivirus of your choice.
9. Restore files from your backup
Also, Windows 8 automatically activates itself. In your case, you shouldn't have any problems. You won't be asked for a Windows 8 product key.
I have not been successful skipping the 8 install and just installing 8.1. I have only been successful installing 8, then upgrading to 8.1.
Possibility #2 - Not likely, but still very possible:
You are experiencing a hardware failure - usually a hard drive. Laptops can get roughed up. Your hard drive may have a fault. If your laptop is free from scrapes, bruises, cuts, contusions, etc... you can have Samsung replace bad parts by paying for the shipping to the repair facility. It won't cost you anything for parts or labor.
If your laptop is under warranty, or you need to know if you're under warranty, you can (sorta) get help from the Samsung chat support technicians. Find them at http://www.samsung.com/us/support/live-chat.html
Access the correct chat by filling in the form:
What product line does your question pertain to (Please select one)? Notebook/Netbook/Ultra Mobile PC
What type of question do you have about your Notebook/Netbook/Ultra Mobile PC? Usage/Operation
After getting on chat myself, I found out the Samsung service center will most likely only install 8 for your laptop if you send it in for repair.
info: Please wait for a Samsung Agent to respond.
info: You are now chatting with 'Saige B'. There will be a brief survey at the end of our chat to share feedback on my performance today.
info: Your Issue ID for this chat is LTK1117901671120X
Visitor: Hi Saige
Saige B: Hi, thank you for reaching out to Samsung technical support. How may I assist you?
Visitor: Hi, I have a Samsung laptop that I've recently upgraded from Windows 8 to Windows 8.1. Ever since then, the computer has been very slow.
Visitor: If I pay to have this laptop shipped to the Samsung repair facility, can Samsung install Windows 8.1 so that it works properly?
Saige B: Could I know the model number of the laptop?
Visitor: I don't have it at the moment, but it's less than a year old.
Saige B: The service center will install the OS that it is purchased with. Have you installed all the drivers from SW update tool?
Visitor: Will the service technicians install Windows 8.1 if requested, even if the laptop originally came with Windows 8?
Saige B: I am afraid; They will install only Windows 8.
Visitor: Ok, thanks a lot for your time today Saige. I appreciate your answers.