Is it possible this sentence to be translated:
You remembered her/his keys OR You remembered their keys.
it's the possessive for the polite person, plural because llaves is plural. Singular would be
Usted recordó su llave
Yes. Possessive adjectives must agree with their object in number and gender.
That possessive adjective doesn't, but the "long form" ones do. Ex: Nuestro, nuestra, nuestros, nuestras. http://www.spanishdict.com/answers/100031/possessive-adjectives#.VNAPeC5GTuR
I think that numbers 1 and 3 mean the same thing. if not can someone please tell me how to say You remembered their keys.
Beforehand, you probably mean "its", not "it's".
Strictly speaking, it's correct, as "sus" can mean his (de él), her (de ella), its (de eso), or your (de usted, i.e. formal "you"). However, I can't even think of one real-life scenario for "usted recordó sus llaves" that would mean "you remembered its keys".
When I listened to the computer and typed what I heard, I typed this: usted recordó sus llaves. It said that my recordó was incorrect though. I don't know why because I compared the spellings and nothing seemed wrong. Although, I did press alt + 0243 to get my ó. Would that be the cause of this? I don't know, but could someone please tell me why it wasn't working/I got it wrong?
Why is it not, "Usted las recordó sus llaves." How do we know when the direct object pronoun is necessary?
Recordar is not reflexive, but acordar is. «Usted recordó / Usted se acordó».
I used "remember" for the verb recordar in a previous example and i got it wrong. What determines this?