Write a polynomial when given a complex and real root

The video tutorial explains how to find a polynomial of degree three given its zeros, including complex zeros. It covers the importance of including conjugates for complex zeros and demonstrates how to convert zeros into factors. The tutorial further explains the multiplication of complex factors using the difference of squares and simplifies the polynomial expression using the FOIL method. The final polynomial is derived with the given zeros.

What must be included when dealing with complex zeros in a polynomial?

• The square of the complex zero

• The conjugate of the complex zero

• The negative of the complex zero

• The reciprocal of the complex zero

How do you express a zero as a factor in a polynomial?

• By setting the zero equal to the polynomial

• By multiplying the zero with the polynomial

• By adding the zero to the polynomial

• By subtracting the zero from the variable and setting it to zero

What technique is used to simplify the multiplication of complex factors?

• The quadratic formula

• The difference of squares

• The Pythagorean theorem

• The binomial theorem

What is the result of multiplying a complex number by its conjugate?

• A real number

• A complex number

• Zero

• An imaginary number

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

• Adding all the factors

• Dividing the factors

• Multiplying the factors

• Subtracting the factors

Which technique is used to expand the expression when forming the polynomial?

• FOIL technique

• Integration

• Completing the square

• Differentiation

What is the degree of the polynomial formed in the tutorial?

• Degree 4

• Degree 3

• Degree 2

• Degree 1