Factorisation of real polynomials over the complex numbers

What this note covers

1. Roots, factors and remainders
2. Polynomial division
3. Conjugate roots
4. Unknown coefficients from remainders
5. Fundamental theorem and multiplicity
6. Complete factorisation and checking
7. Construct and audit a real polynomial from complex roots
8. Recover unknown coefficients from roots and remainders

8 sections · 10 key terms & formulas · 6 common mistakes