could have, not could of

In speech, have is sometimes shortened to 've, which sounds like of. As a result, people sometimes mistakenly write could of, might of, should of, would of and other similar phrases instead of the correct verb forms could have, might have, etc.

Remember that you need to use the verb have or the contraction 've with a past participle.

I could have (not could of) had a better lunch somewhere else.
     [could have + past participle had]

If Alice had had enough money, she might have (not might of) agreed to eat at another restaurant.

We should've (not should of) avoided this fast-food place.

I would've (not would of) liked roast beef, but I had to settle for a burger and fries.