How to write the polynomial given zeros with multiplicity

The video tutorial explains how to handle zeros in polynomial equations by setting them as factors and understanding the concept of multiplicity. It covers the importance of complex conjugates for imaginary zeros and rational zeros. The tutorial also demonstrates how to write factors and multiply them to form polynomials, using methods like the box method for efficient calculation.

What is the first step when given zeros in a problem?

• Set them equal to Y

• Set them equal to X

• Ignore them

• Multiply them directly

What does a multiplicity of two indicate about a zero?

• The zero is rational

• The graph crosses the zero

• The graph bounces at the zero

• The zero is imaginary

Why is it necessary to consider complex conjugates for imaginary zeros?

• To increase the degree of the polynomial

• To decrease the degree of the polynomial

• To ensure the polynomial is real

• To simplify the polynomial

How do you determine the power to raise a factor when considering multiplicity?

• By the number of zeros

• By the multiplicity value

• By the degree of the polynomial

• By the value of the zero

What is the result of multiplying X - 1 by itself?

• X^2 - 2X + 1

• X^2 + 1

• X^2 - 1

• X^2 + 2X + 1

Which method is preferred by the teacher for multiplying factors?

• Substitution method

• Graphical method

• Box method

• FOIL method

What is the final polynomial obtained in the example provided?

• F(x) = X^4 - 2X^3 + 10X^2 - 18X + 9

• F(x) = X^4 + 2X^3 - 10X^2 + 18X - 9

• F(x) = X^4 + 2X^3 + 10X^2 - 18X - 9

• F(x) = X^4 - 2X^3 - 10X^2 + 18X + 9