I made this with the intention of grouping students into groups of 3. There are two versions- 1 is where you're able to find the zeros of the function without using the rational zeros theorem and synthetic division, the other requires it. Only one problem in each version, but both are broken down in parts so that the students can see the importance of each step.
After the groups are done (I pass out both versions), I ask the groups to find the other groups with the same function to compare answers/graphs. I think this step is so important because it allows the students to discuss and collaborate in larger groups. (I wholeheartedly believe that collaborating and discussions help instill freshly learned concepts.)
Afterwards, we compare the graphs as a class, either on the board, or on desmos (free online graphing calculator) through the projector. If we look at the functions through desmos, we can even check to see if the function written as a product of linear factors overlaps with the polynomial function given! I usually ask the students what they got for the factors to verify this. :)