Many students find polynomial functions tricky. This can sometimes lead to big mistakes that make it harder for them to understand and solve problems. Here are some common errors:

• Ignoring the Rational Root Theorem: Students often forget about possible rational roots. This can cause them to come up with incorrect factorizations.

• Misapplying Synthetic Division: Some students make mistakes when doing synthetic division. This can happen from either miscalculating or misunderstanding the steps.

• Forgetting Degree and Leading Coefficient: Not realizing that the degree of a polynomial impacts how its graph behaves can lead to wrong graphing.

To get better at this, students should:

• Practice using the Rational Root Theorem regularly.
• Carefully check each step when doing synthetic division.
• Always think about how the degree and leading coefficient affect the polynomial for a better understanding.