How to Find All of the Zeros of a Polynomial by Factoring, Including Imaginary

The video tutorial covers solving polynomial functions, focusing on factoring and the zero product property. It explains the use of synthetic division and the rational zero test. The tutorial introduces imaginary numbers when dealing with square roots of negative numbers and discusses the importance of writing linear factors correctly. The fundamental theorem of algebra is explored, emphasizing the types of zeros: rational, irrational, and complex, and their relationship to the degree of the polynomial.

Describe the process of solving for zeros of a polynomial when it is in factored form.

What are the implications of having a polynomial function with a degree of 3 in terms of its zeros?

Why do complex zeros always come in pairs? Explain the reasoning behind this.