[1][2] Minchew attended Langley High School in Fairfax County, Virginia; as a senior, he was a campaign volunteer for future Congressman Frank Wolf.
from Washington and Lee University School of Law in 1984, after which he clerked for Supreme Court of Virginia Justice Christian Compton.
[3][4] The 10th House district was moved from the Martinsville area, on Virginia's southern border, to the northern tip of the state in the 2011 redistricting.
Minchew won a three-way Republican primary in the new district, defeating his closest competitor, attorney John Whitbeck, by 87 votes.
In the general election he faced Democrat Peter Rush, a Leesburg resident and formerly a member of the Loudoun County Soil and Water Board.
[12] In 2017, Minchew was defeated in his bid for a fourth term in the Virginia House of Delegates, losing to Democratic candidate Wendy Gooditis 15,151-14,014.