Math9-12+
Factoring and Solving Polynomials Practice Set
By Jeffrey K.
A 10-problem practice worksheet in which 10th graders find the factors and real zeros of a variety of polynomial functions, using methods such as factoring by grouping, the Rational Root Theorem, and synthetic division. Students show all work and explain their chosen method, making it well suited to a single class period or as homework reinforcement.
Customize for your classroom
Teacher Guide & Tips
- Use this set after students have practiced factoring trinomials and reviewed the Strategy Guide, typically as a 45 to 60 minute independent or partner practice block.
- Discussion question: How do you decide whether to factor by grouping, use the Rational Root Theorem, or try synthetic division for a given polynomial?
- Scaffold for struggling readers: Have them first list the number of terms and check for a GCF before choosing a method, and provide a worked example of synthetic division with a simple cubic.
- Extension for advanced students: Ask them to write a degree-4 polynomial with specified zeros and verify it by expanding and solving, or to explain why a polynomial with a complex zero must also have its conjugate.
- Estimated time: about 5 minutes per problem for most students, so roughly 50 minutes total including the explanation requirements.
Math9-12+
Factoring and Solving Polynomials Practice Set
By Jeffrey K.
A 10-problem practice worksheet in which 10th graders find the factors and real zeros of a variety of polynomial functions, using methods such as factoring by grouping, the Rational Root Theorem, and synthetic division. Students show all work and explain their chosen method, making it well suited to a single class period or as homework reinforcement.
Customize for your classroom
Teacher Guide & Tips
- Use this set after students have practiced factoring trinomials and reviewed the Strategy Guide, typically as a 45 to 60 minute independent or partner practice block.
- Discussion question: How do you decide whether to factor by grouping, use the Rational Root Theorem, or try synthetic division for a given polynomial?
- Scaffold for struggling readers: Have them first list the number of terms and check for a GCF before choosing a method, and provide a worked example of synthetic division with a simple cubic.
- Extension for advanced students: Ask them to write a degree-4 polynomial with specified zeros and verify it by expanding and solving, or to explain why a polynomial with a complex zero must also have its conjugate.
- Estimated time: about 5 minutes per problem for most students, so roughly 50 minutes total including the explanation requirements.