Lesson Plan: Partial Fractions: Nonrepeated Irreducible Quadratic Factors
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to decompose rational expressions into partial fractions when the denominator has nonrepeated irreducible quadratic factors.
Objectives
Students will be able to
- decompose a rational expression with an irreducible quadratic factor in the denominator,
- decompose a rational expression with an irreducible repeated quadratic factor in the denominator,
- decompose rational expressions with irreducible quadratic factors in the denominator by first applying algebraic division to lower the degree of the numerator,
- use a given partial fraction decomposition involving an irreducible repeated quadratic factor in the denominator to find unknowns.
Prerequisites
Students should already be familiar with
- prime polynomials and using discriminants,
- partial fraction decomposition with linear factors and repeated factors,
- algebraic division and synthetic division.
Exclusions
Students will not cover
- partial fraction decomposition without an irreducible quadratic factor in the denominator.
