What’s the best way to improve credit score in less than 4 months if I currently only have one credit card?

I have paid off and closed all of my accounts (student loans, car, credit cards) except one credit card that has a small balance. I am virtually debt free. I do have some bad items on my credit report but they are greater than 2 years old and most are greater than 4-5 years old. My medium score is 714 and I’m trying to raise that to above at LEAST 720 in 4 months, and preferably above 740 so I can get the best interest rate on a new home I’m buying. I’ve read articles that said I shouldn’t have closed all of my accounts – that it’s best to have 3 accounts open, all with small balances to show that you know how to manage your debt. My loan officer said I should run out and open up 2 more accounts, but this sounds weird. Won’t those inquiries negatively affect my credit? I guess my question is: what’s best? Open up 2 more accounts or just pay off my one small remaining balance, keep that card open, and just sit tight?

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