Agenda, Semester Week 5

Polynomials and Induction

This week will finalize our study of polynomials. The division algorithm for polynomials will be treated for determination of the multiplicity of a root of a polynomial.

Another topic that will be covered this week is induction, a method of proof that relies on recursive definitions. At its core, induction is a compact technique to verify whether certain proposed expressions indeed are valid.

Key Terms

The division algorithm for polynomials. Factors in a polynomial and the factorized form of a polynomial. Multiplicity of roots. Induction.

Preparation and Syllabus

This week will cover Sections 5.5 and 5.6 from Chapter 5 as well as Sections 3.3 through 3.5 from Chapter 3 in [the textbook].

Exercises

Exercises for Long Day.

Exercises for Short Day.