1. 3.6 Complex Zereos

2. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have at least one complex zero. Remember real numbers like 7 can be considered complex when written as 7 + 0i. So any polynomial will have complex zeros. The degree of the polynomial tells you exactly how many complex roots exist Even degree polynomials may have no real roots while odd degree must have one real root. Remember, Imaginary roots exist in pairs.

3. The Complete Factorization Theorem The Complete Factorization Theorem states that for any polynomial with degree 1 or greater the polynomial can be written as P(x) = a(x – c1) (x – c2) (x – c3).... (x – cn) where a and c1, c2, c3,... cn are complex numbers. This means that a polynomial can be written in factored form.