Polynomial Functions and Their Properties

The video tutorial explains how to find the equation of a polynomial function with real coefficients, given specific zeros, including a zero with multiplicity and complex zeros. It covers the formation of polynomial factors, multiplication of binomials, and simplification by combining like terms. The tutorial concludes with deriving the final polynomial function and verifying it graphically.

What is the multiplicity of the zero 2 in the given polynomial function?

• 3

• 2

• 4

• 1

If -1 - 2i is a zero of a polynomial, what must also be a zero?

• -1 + 2i

• 2 - i

• 1 - 2i

• 1 + 2i

How many zeros does the polynomial have, considering the given zeros and their multiplicities?

• 5

• 4

• 3

• 2

What is the first step in forming the polynomial from its zeros?

• Create factors from the zeros

• Add the zeros together

• Multiply the zeros

• Divide the zeros by 2

What is the result of multiplying (x - 2) by itself?

• x^2 - 4

• x^2 + 4

• x^2 - 2x

• x^2 - 4x + 4

What is the value of i squared?

• 1

• -1

• i

• 0

What is the degree of the polynomial function formed?

• 2

• 3

• 5

• 4

What happens at the x-axis for a zero with multiplicity 2?

• The graph crosses the x-axis

• The graph forms a loop at the x-axis

• The graph does not touch the x-axis

• The graph touches but does not cross the x-axis

Why do complex zeros not produce x-intercepts?

• They are integers

• They are imaginary

• They are real

• They are rational

What is the constant term in the final polynomial function?

• 20

• 25

• 15

• 10