Motor Variable - Polynomial Factorization

Polynomial Factorization

Two staples of introductory algebra include factorization of polynomials and the fundamental theorem of algebra. With the adoption of motor variables the traditional expectations are countered. The reason is that (D, +, × ) does not form a unique factorization domain. Substitute structures for the motor plane were provided by Poodiack and LeClair in 2009. They prove three versions of the fundamental theorem of algebra where a polynomial of degree n has n2 roots counting multiplicity. To provide an appropriate concept for multiplicity, they construct a matrix which contains all the roots of a polynomial. Furthermore, their method allows derivation of a similar theorem for polynomials with tessarine coefficients. The article in The College Mathematics Journal uses the term "perplex number" for a motor variable, and the term "hyperbolic number" for a tessarine. A basic example of the non-unique factorization is

exhibiting the set {1, −1, j, −j } of four roots to the second degree polynomial.