Abstract Algebra | Corollaries and examples of the division algorithm for polynomials.

We give some corollaries and examples of the division algorithm for polynomials. In particular, we prove that if a is a root of f(x) then f(x)=(x-a)g(x), if a is a double root of f(x) then it is a root of f'(x), and that a degree n polynomial can have at most n roots. Further, we give some examples of applying the division algorithm to polynomials over various fields. Please Subscribe: https://www.youtube.com/michaelpennma... Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathem... Research Gate profile: https://www.researchgate.net/profile/... Google Scholar profile: https://scholar.google.com/citations?...