All that is necessary for a valid contract is that there be an offer by one party, acceptance of that offer by other (this is also referred to as a "meeting of the minds"--i.e. that the two parties agreed on the terms), and an exchange of "consideration," or things or promises of value. A bill of sale signed by the two parties would create an enforceable contract: the fact that they signed it shows the meeting of the minds (they both agreed to the terms) and the fact that there was payment or a promise  to pay for a used car is the exchange of consideration.As a general matter, contracts do NOT need to be notarized, and notarizing them doesn't add anything legally, though it does add a way to help prove factually that a person signed it, if he or she tries to later claim that he or she did not and someone else forged the signture. Only a few special documents, like wills (in many states) actually have to be notarized.