Polynomial Operations and Complex Zeros

The video tutorial explains how to find a polynomial function with real coefficients given specific zeros, including complex zeros. It covers the concept of complex conjugates, the relationship between zeros and polynomial factors, and the process of simplifying and multiplying these factors. The tutorial concludes with combining like terms to form the final polynomial equation.

What is the degree of the polynomial function if it has zeros at +3, -1, and 4 + 2i?

• 2

• 3

• 5

• 4

If a polynomial has a complex zero of 4 + 2i, what must also be a zero?

• -2 - 4i

• 2 + 4i

• -4 + 2i

• 4 - 2i

What factor corresponds to a zero of -1 in a polynomial function?

• x - 1

• x + 1

• x + 2

• x - 2

How do you express the factor for a complex zero of 4 + 2i?

• x - 4 + 2i

• x + 4 + 2i

• x + 4 - 2i

• x - 4 - 2i

What is the first step in multiplying binomial factors to form a polynomial?

• Multiply all factors at once

• Multiply two factors at a time

• Add the factors

• Divide the factors

When simplifying the polynomial, what happens to terms like +2xi and -2xi?

• They cancel each other out

• They divide

• They multiply

• They add up

What is the value of i squared in complex numbers?

• 0

• -1

• i

• 1

What is the result of combining the terms 20x^2, 16x^2, and -3x^2?

• 43x^2

• 39x^2

• 36x^2

• 33x^2

What is the final constant term in the polynomial after simplification?

• -60

• -40

• -20

• 0

What is the leading term of the polynomial function?

• x^2

• x^3

• x^4

• x^5