Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains how to find the remaining zeros of a polynomial when one zero is a complex number, specifically 2i. The instructor demonstrates using synthetic division to handle complex zeros and shows that if 2i is a zero, then -2i must also be a zero. The process involves performing synthetic division twice, first with 2i and then with -2i, to simplify the polynomial and find the remaining zeros. The final zeros identified are 2i, -2i, 1, and -1/2. The tutorial emphasizes that synthetic division can be used effectively with complex numbers.

What is the initial step when dealing with a complex zero in a polynomial?

• Use the quadratic formula

• Factor the polynomial

• Graph the polynomial

• Apply synthetic division

When performing synthetic division with 2i, what is the result of multiplying 2 by 2i?

• 8i

• 4i

• 2i

• 4

What must also be a zero if 2i is a zero of the polynomial?

• -2

• -2i

• 2

• i

What is the final polynomial equation after using synthetic division with -2i?

• 2x^2 - 1 - 1

• 2x^2 - 1

• x^2 + 1

• x^2 - 2x + 1

What are the zeros of the polynomial after completing the synthetic division process?

• 2i, -2i, 1, -1/2

• 2i, -2i, 0, 1

• 2i, -2i, 1, 1/2

• 2i, -2i, -1, 1/2