Lesson Plan

Synthetic Division and the Factor Theorem


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Big Ideas




This lesson is going to build on the concept of polynomials and their roots. Students will:

  • illustrate the relationship between roots and factors. [IS.3 - Struggling Learners]

  • use synthetic division to determine if a certain value is a root of a polynomial. [IS.4 - Struggling Learners]

Essential Questions

  • How can we determine if a real-world situation should be represented as a quadratic, polynomial, or exponential function?

  • How do you explain the benefits of multiple methods of representing polynomial functions (tables, graphs, equations, and contextual situations)?


  • Factor: One of two or more expressions that are multiplied. [IS.1 - Struggling Learners]

  • Fundamental theorem of algebra: Every polynomial equation of degree n ≥ 1, with complex coefficients, has at least one root which is a complex number (real or imaginary).

  • Root: The solution to a given equation.

  • Synthetic division: A short way of dividing a polynomial by a binomial.

  • Remainder: In division, the difference of the dividend minus the product of the quotient times the divisor.

  • Zero of a function: The value of the argument for which the function is equal to zero; also the Root of the function and the Solution to the equation. [IS.2 - Struggling Learners]


90–120 minutes [IS.5 - All Students]

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