The Factor Theorem can help you get better at graphing polynomials, but it has some challenges:

1. Limited Use: It only works for polynomials that can be factored. This means students might find it hard when dealing with more complicated ones.

2. Calculation Mistakes: Errors in synthetic division or checking polynomials at certain points can lead to wrong answers about factors and how often they repeat.

3. Understanding Roots: Some students might not get rational roots correctly, making graphing tougher.

Solutions:

• Practice: Doing exercises often can help you understand how polynomials behave.
• Use Technology: Graphing software can help you see how functions look and check your results.