Understanding Complex Zeros in Polynomials

This video tutorial explains how to find the remaining zeros of a polynomial when given an imaginary or complex zero. It covers the concept of conjugate pairs, demonstrates synthetic division with complex numbers, and shows how to multiply complex numbers during the process. Finally, it explains how to find the remaining zeros using factoring and the quadratic formula.

What is the relationship between complex zeros in a polynomial with real coefficients?

• They always appear as single entities.

• They appear as conjugate pairs.

• They are always real numbers.

• They do not affect the polynomial.

What is the first step in synthetic division when given a complex zero?

• Divide the coefficients.

• Add the coefficients.

• Multiply the coefficients.

• Drop down the first coefficient.

What should be done if a term is missing in the polynomial during synthetic division?

• Multiply the coefficients.

• Ignore the missing term.

• Subtract the coefficients.

• Add a zero as a placeholder.

During synthetic division, what operation is performed after multiplying on the diagonal?

• Subtract straight down.

• Add straight down.

• Multiply straight down.

• Divide straight down.

What is the result of multiplying 1 + i with -1 - i during synthetic division?

• 2

• -2i

• -1

• 0

What is the next step after completing synthetic division with 1 + i?

• Solve the quadratic equation.

• Multiply the results.

• Add the results.

• Perform synthetic division with 1 - i.

What is the significance of the remainder being zero in synthetic division?

• It indicates a calculation error.

• It confirms the divisor is a zero of the polynomial.

• It means the polynomial is irreducible.

• It shows the polynomial has no real zeros.

What is the quadratic equation obtained after synthetic division with 1 - i?

• x^2 + 2x - 1

• x^2 - x - 2

• x^2 + x + 2

• x^2 - 2x + 1

What are the remaining zeros of the polynomial after solving the quadratic equation?

• x = 2 and x = 1

• x = 1 and x = -2

• x = 2 and x = -1

• x = -1 and x = 1

If factoring the quadratic equation is not possible, what method can be used to find the zeros?

• Synthetic division

• Quadratic formula

• Graphical method

• Long division