Finding the Zeros Given One Complex Zeros

The video tutorial explains how to handle complex zeros in polynomials, focusing on using synthetic and long division. It begins by identifying complex zeros and their conjugates, then demonstrates multiplying these conjugates to eliminate imaginary parts. The tutorial proceeds to apply long division to find polynomial factors and zeros, emphasizing the importance of identifying all zeros for polynomial equations.

What is the conjugate of the complex number 5 + 2i?

• 5 + 2i

• 5 - 2i

• 5 + 3i

• 5 - 3i

Explain the process of synthetic division as mentioned in the text.

What happens when you multiply a complex number by its conjugate?

How do you rewrite the expression using the associative property?

What is the result of multiplying (X - 5)^2 and (2i)(-2i)?

Describe the long division process used for the polynomial X^3 - 7X^2 - X + 87.

What is the final factor obtained after performing the long division?