When I give talks in similar situations, I typically assume that at least some of the audience members will be unfamiliar with much of what I think of as basic. Your job is to "remind" them, without spending excessive time on the topic. A good place to use this technique is with definitions. For instance: "... a polynomial, for example 3x4-5x2+2x+6." (The best way to teach most things, particularly definitions and algorithms, is with examples.) You can do this fairly unobtrusively, so that those who don't recall the definition are reminded, while those who do are still not offended.
Another point to remember is that generally, it's good for some of your talk to be a refresher. You might say something like "most of you are probably familiar with this, but just to make sure we're all on the same page..." This material shouldn't be the majority of your talk, but 5 or 10 minutes of this is often very appropriate, say in a 25 minute talk.
In most talks I start by saying: "If you have questions as we go along, please ask." If you get many questions on material that you think of as basic, be ready to slow your pace. A variation on this is to have some worked examples early in your talk. Give the audience time to think about a question, then ask audience members for the answer before revealing it on your slides. Their responses (especially nonverbal) can give you a good sense of who knows what. Typically, I talk with slides, but answer miscellaneous questions on a whiteboard.
A final option is to get to the room early, and try to talk one-on-one with the audience members, as they arrive. If you ask them then, you may be more likely to get an honest answer. Another version of this is to ask the seminar organizer (or whoever schedule you to give the talk) what knowledge they think is reasonable to assume of the audience.
- Make educated guesses beforehand about what your audience knows (typically less than you would think), asking them (or the organizer) if possible.
- Make liberal use of examples and "parenthetical explanations".
- Plan for 20-30% of your talk to be review.
- Adapt the speed of your presentation based on the feedback you get during the talk.