To finish out of hand. In allusion to articles polished.
Iʹll polish him off in no time means Iʹll set him down, Iʹll give him a drubbing.
To polish off a meal is to eat it quickly, and not keep anyone waiting.
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Entry taken from Dictionary of Phrase and Fable, edited by the Rev. E. Cobham Brewer, LL.D. and revised in 1895.
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