How to Use Synthetic Division and Factoring to Find All the Real and Complex Zeros

The video tutorial covers the importance of the rational zero test and how to identify rational zeros using graphing technology. It explains the process of using synthetic division to find factors and zeros of a polynomial. The tutorial also demonstrates the square root method to find complex zeros and emphasizes the importance of including both positive and negative roots. The concept of conjugate pairs is introduced, highlighting the necessity of considering both positive and negative imaginary parts when dealing with complex numbers.

What is the importance of the rational 0 test in polynomial problems?

Explain the process of using synthetic division when a rational zero is found.

How do you find all the zeros of a polynomial when one factor is known?

What is the significance of including ± when taking square roots in polynomial equations?

Describe what conjugate pairs are in the context of polynomial roots.