The UVic Writer's Guide
Could of, Would of, Should of, etc.
Yes, it sounds like this in casual conversation, but the correct
spelling is "could have, would have," etc. It is an error guaranteed
to raise your intructor's hackles. ("Hackles" are the long feathers
on a cock's neck; the bird raises them in anger.) If you are reporting
dialogue, and want to retain a colloquial flavour, use "could've".
Dictionary of Usage
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Copyright, The Department of English, University of Victoria,
This page updated September 22, 1995