Given One Complex Zero Find the Remaining Zeros of a Polynomial

The video tutorial explains how to find the remaining zeros of a polynomial when given a complex zero. It introduces the concept of conjugate pairs and demonstrates the use of synthetic division with complex numbers. The instructor provides a detailed walkthrough of the synthetic division process, emphasizing the arithmetic operations involved. Finally, the tutorial concludes with identifying the remaining zeros and factors of the polynomial.

What is the relationship between a complex zero and its conjugate in a polynomial?

• They are always equal.

• They are always opposite in sign.

• They cannot both be zeros.

• They are both zeros of the polynomial.

What is the main purpose of using synthetic division in this context?

• To determine the leading coefficient.

• To find the degree of the polynomial.

• To simplify the polynomial.

• To find the remaining zeros of the polynomial.

When performing synthetic division with complex numbers, what operation is primarily used?

• Subtraction

• Division

• Addition

• Exponentiation

What is the result of multiplying two imaginary units, i.e., i * i?

• 1

• -1

• i

• 0

What is the final factor obtained after performing synthetic division twice in this example?

• x + 5i

• x - 5i

• 2x + 3

• x - 3