  We show that any matrix-polynomial combination of free noncommutative random
variables each having an algebraic law has again an algebraic law. Our result
answers a question raised by a recent paper of Shlyakhtenko and Skoufranis. The
result belongs to a family of results with origins outside free probability
theory, including a result of Aomoto asserting algebraicity of the Green
function of random walk of quite general type on a free group.
