It depends on the seriousness of the past problems and the accuracy of the credit report. If you believe there is inaccurate information on your credit report, you should follow the proper procedures to dispute the errors. You can find out how to dispute errors here:

If the negative information is accurate, the Fair Credit Reporting Act also prevents certain credit information from being included on consumer reports if that information is more than seven or ten years old, depending on the type of debt.

(15 U.S.C. §1681c)