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 purpose of the rational zero test?

• To find irrational zeros

• To identify potential rational zeros

• To solve quadratic equations

• To graph complex numbers

Which method is preferred for dividing polynomials in the video?

• Synthetic division

• Graphical division

• Factorization

• Long division

If 5 is a zero of the polynomial, what is one of its factors?

• X^2 - 5

• X^2 + 5

• X - 5

• X + 5

What method is used to find complex zeros in the video?

• Square root method

• Rational zero test

• Graphing

• Synthetic division

Why is it important to include both positive and negative roots when solving for zeros?

• To avoid complex numbers

• To ensure all zeros are found

• To use graphing technology

• To simplify the polynomial