Is the past tense of the word "cost" remain "cost"?
If it's being used as a verb, the past tense of "cost" is "costed". But as an adjective (which is how it's normally used) the word won't change dependent on tense.
Let's find out!
Let's run through a couple of sentences in different tenses:
Present - What does this cost?
Future - What will this cost?
Past - What did that cost?
Now, to be fair, the reason the word isn't changing is because I'm not using it as a verb - it's being used as an adjective (we're talking about an aspect of the pronoun "that").
Now let's use it as a verb:
Present - When we cost the additional factors, our product is selling at a loss.
Future - When will we cost the additional factors?
Past - When we costed an amended list of factors, we created a net profit.
Aside from the awkward sentences, we can see that the verb "cost" will have a past participle of "costed".
It's because the word "cost" is a bit awkward in the role of verb that it's typically used as an adjective.