Hey Kweennxhanxes. Let me help you on this question.
If we take a closer look at both mushrooms, yeast, and mold, we will notice one similarity between all of them.
For example, all of the living organisms you listed are eukaryotic - containing nucleus and other inbound organelles most bacteria doesn't have. Their cell walls are not composed chitin, and not cellulose like plants and other organisms (we, as animals, don't have cell walls). Did you know that chitin is much more likely to lose shape; however, it requires almost no ATP to produce and restore. These organisms are also performing something called "extracellular digestion" - digesting anything outside with different enzymes - yikes!
As you can see, all of these characteristics are shared are within a certain Kingdom called "Fungi", which is actually separate from both plants, animals, etc.
Answer: Mushrooms, yeast, and mold are part of the kingdom called "Fungi"