When You Have One Complex Zero Find the Remaining Zeros of the Polynomial

The video tutorial explains how to use synthetic division to find zeros of a polynomial. It begins by discussing the concept of synthetic division and how a given zero can be used to divide a polynomial, resulting in a remainder of zero. The instructor provides a detailed example, demonstrating the calculation process. The tutorial then explores how to find remaining zeros by factoring the polynomial further. The video concludes with a discussion on setting factors equal to zero to find the final answer.

What is the result of synthetic division when a zero is correctly used?

• A remainder of 1

• A remainder of 0

• A quotient of 0

• A factor of 1

Why is it important to find all zeros of a polynomial?

• To determine the polynomial's degree

• To find the polynomial's leading coefficient

• To simplify the polynomial

• To fully factor the polynomial

If 3i is a zero of a polynomial, what else must be a zero?

• 3

• -3i

• i

• -i

What is the purpose of setting a factor equal to zero in polynomial division?

• To simplify the polynomial

• To determine the polynomial's leading coefficient

• To find the zeros of the polynomial

• To find the polynomial's degree

In the example given, what is the final step to find the zeros of the polynomial?

• Divide the factors

• Add the factors

• Set the factor equal to zero

• Multiply the factors