Polynomial Functions and Complex Zeros

The video tutorial explains how to find a degree three polynomial function with real coefficients given specific zeros and a vertical intercept. It covers identifying zeros, including complex conjugates, forming the polynomial, simplifying it, and determining the constant 'a' using the vertical intercept. The process involves multiplying binomial factors, simplifying terms, and using algebraic techniques to solve for the polynomial function.

What is the degree of the polynomial function we are asked to find?

• Degree 3

• Degree 5

• Degree 4

• Degree 2

Which of the following is a zero of the polynomial function?

• x = 5

• x = 2

• x = -1

• x = 3

What is the conjugate of the complex zero -3 - 5i?

• -3 + 5i

• -3 - 5i

• 3 + 5i

• 3 - 5i

How many binomial factors are needed for a degree three polynomial?

• One

• Two

• Three

• Four

What is the result of multiplying x by x in the simplification process?

• x

• x^4

• x^3

• x^2

What does the term -25i^2 simplify to?

• 0

• 25

• -25

• -50

What is the value of 'a' when using the vertical intercept?

• -1

• -4

• -2

• -3

What is the vertical intercept of the polynomial function?

• (0, -34)

• (0, -50)

• (0, -100)

• (0, -68)

What is the coefficient of x^2 in the final polynomial function?

• 14

• 7

• -7

• -14

What is the constant term in the final polynomial function?

• -100

• -80

• -68

• -34