Now in Shushan the palace there was a certain Jew, whose name was Mordecai, the son of Jair, the son of Shimei, the son of Kish, a Benjamite; Esther 2:5 (KJV)
Statement: There is an error in the bible because Esther 2:5 says Mordecai was both of the tribe of Judah (a Jew) and of Benjamin (a Benjamite). The original Hebrew also supports this reading -- אִ֣ישׁ יְהוּדִ֔י (’îš yə-hū-ḏî, "of Judah") and אִ֥ישׁ יְמִינִֽי׃ (’îš yə-mî-nî, "of Benjamin").
Answer: Referring to a Hebrew of any tribe as a "Jew" became a technicality (a convention of speech) after the loss of the Ten Tribes of Israel. This is made more apparent in modern translations such as the NIV, NLT, ISV, and NET bible. ex. Esther 2:5 (NIV) has "Now there was in the citadel of Susa a Jew of the tribe of Benjamin, ... "
In common speech, the word "Jew" is used to refer to all of the physical and spiritual descendants of Jacob/Israel, as well as to the patriarchs Abraham and Isaac and their wives, and the word "Judaism" is used to refer to their beliefs. Technically, this usage is inaccurate, just as it is technically inaccurate to use the word "Indian" to refer to the original inhabitants of the Americas. However, this technically inaccurate usage is common both within the Jewish community and outside of it, and is therefore used throughout this site.http://www.jewfaq.org/whoisjew.htm
Question: How did this become a convention of speech?
Answer: After the Assyrians carried away Northern Israel, Southern Israel became known as the Kingdom of Judah. This was at about the time of Jeroboam and Rehoboam. All the remaining Hebrews began to be called Jews after the name Kingdom of Judah, not necessarily the Tribe of Judah. Thus we call all members of various tribes today Jews by convention, even though they may be of a different tribe such as Benjamin.
After Saul died, all the tribes other than Judah remained loyal to the House of Saul, but after the death of Ish-bosheth, Saul's son and successor to the throne of Israel, the Tribe of Benjamin joined the northern Israelite tribes in making David — then king of Judah — king of the united Kingdom of Israel and Judah. On the accession of Rehoboam, David's grandson, in c. 930 BCE the northern tribes split from the House of David to reform (sic) a Kingdom of Israel. The Tribe of Benjamin remained a part of the Kingdom of Judah until Judah was conquered by Babylon in c. 586 BCE and the population deported.https://en.wikipedia.org/wiki/Tribe_of_Benjamin
Originally, the term Yehudi referred specifically to members of the tribe of Judah, as distinguished from the other tribes of Israel. However, after the death of King Solomon, the nation of Israel was split into two kingdoms: the kingdom of Judah and the kingdom of Israel (I Kings 12; II Chronicles 10). After that time, the word Yehudi could properly be used to describe anyone from the kingdom of Judah, which included the tribes of Judah, Benjamin and Levi, as well as scattered settlements from other tribes. **The most obvious biblical example of this usage is in Esther 2:5, where Mordecai is referred to as both a Yehudi and a member of the tribe of Benjamin.** //(Emphasis Added)//
In the 6th century B.C.E., the kingdom of Israel was conquered by Assyria and the ten tribes were exiled from the land (II Kings 17), leaving only the tribes in the kingdom of Judah remaining to carry on Abraham's heritage. These people of the kingdom of Judah were generally known to themselves and to other nations as Yehudim (Jews), and that name continues to be used today.
http://www.jewfaq.org/whoisjew.htm