Yes, but David was not a Jew. This may help:
Genesis: God, Adam, Eve, Cain, Abel, Seth, Enoch, Methuselah, Noah, Shem, Ham, Japheth, Lot, Abraham, Sara, Melchizedek, Eliezer, Hagar, Ishmael, Isaac, Abimelech, Rebekah, Laban, Keturah, Esau, Jacob/Israel, Leah, Rachel, Reuben, Simeon, Levi, Judah, Dan, Naphtali, Gad, Asher, Issachar, Zebulun, Joseph, Benjamin, Dinah, Potiphar, Tamar, Perez, Zerah, Manasseh, Ephraim.
Exodus: Moses, Zipporah, Gershom, Jethro, Aaron, Eleazar, Joshua, Hur, Nadab, Abihu, Ithamar, Bezalel, Uri, Nun, Oholiab, Ahisamach.
Leviticus: Mishael, Elzaphan, Uzziel, Molech, Shelomith, Dibri.
Others: David, Solomon and Sampson were not Jews, among many others...
No Israelites were called "Jews" until well after the collapse of the original Davidic Kingdom of Israel and formation of the Northern and Southern Kingdoms in about 922 BC. Many scholars place the earliest date of actual word usage ~500 BC, following the return of the Southern Kingdom from Bablyon. Those ~50,000 Jews were Israelites, but only a tiny number of the Millions of Israelites were called Jews. While the numbers are relatively small, the distinction is a major one.