Chapter 3
Polynomials


  1. The notion of a polynomial

  2. Division of polynomials

  3. Polynomial functions

  4. Factorization

  5. Shift registers

  6. Exercises

  7. Summary of Chapter 3

In this chapter we extend calculation with integers to calculation with polynomials, expressions in which beside scalars (from Z, Q, R, C, Z/nZ) also an indeterminate occurs. You have already seen such polynomials when solving quadratic equations and plotting graphs of quadratic functions. For polynomials we introduce concepts related to the concept's divisor, gcd, etc., which we have introduced for integers in Chapter 1.

Section 3.1
The notion of a polynomial
  1. The notion
  2. Sum and product
Section 3.2
Division of polynomials
  1. Leading term and degree
  2. Division with remainder
  3. Gcd and lcm
  4. Euclid's algorithm
  5. Characterization of the gcd
Section 3.3
Polynomial functions
  1. The notion
  2. Interpolation
Section 3.4
Factorization
  1. Irreducible polynomial
  2. Relatively prime
  3. Unique factorization
Section 3.5
Shift registers
  1. The notion
  2. Output formula
  3. Linear algebra