From questions like this in DuoLingo I realized that I, a native speaker who knows well when to add a copula and when not to, don't know the rules and can't figure them out.
Here, what copula would you add? זה would be funny, doubling the word. I can actually imagine people doing it in speech, but it would be a mark of "weak language" and bad education.
What about adding הוא? Interestingly, it used to be done, but the two words were contracted: זהו זית. In female, formal: זוהי (a contraction of זו היא). I think both are nowadays very formal. The Female colloquial form זאתי (from זאת היא) is still used, I think (and still colloquial). The plural "אלה הם" still sounds perfectly good (אלה הם הזיתים הכי טעימים, אלה הזיתים הכי טעימים - both sound equally good to me).
Confused you enough?