Put these together as an extension activity for my students on factoring. Each set is designed so that every polynomial is a possible answer, depending on students’ interpretation and knowledge.
I have a few goals with this. First, I want students to slow down and consider the properties of polynomials, rather than just rushing through and factoring. Second, I want them to examine some structures that can allow a polynomial that looks complicated to be factored quickly and easily — these are properties that polynomials have in common but may not be apparent at first glance. Finally, I want students to get practice factoring and analyzing a variety of polynomials. There are a number in here that I doubt they will be able to solve and I put some in for my amusement, but this range would make this a useful formative assessment tool for an Algebra II class or higher.
I think one important part of this activity is to structure it so that students have an incentive to slow down. I would put students in groups, and assign each student a polynomial, asking them to argue for why it doesn’t belong. Alternatively, students could be asked to come to an agreement on which polynomial doesn’t belong before moving on. I could also see this being used in a Talking Points structure a la Elizabeth Statmore, or a gallery walk around the room.
Enjoy! I’ll report back once I’ve used these with students.