Given a Complex Zero Use Synthetic Division to Find All of the Zeros for a Polynomial

The video tutorial explains how to find the zeros of a polynomial using synthetic division. It begins with an introduction to the concept of polynomial zeros and the importance of synthetic division. The instructor demonstrates the process of synthetic division, including handling complex numbers and their conjugates. The tutorial concludes with a summary of the steps to find all zeros, emphasizing the role of synthetic division in simplifying the process.

What method is used to determine if a given value is a zero of a polynomial?

• Synthetic division

• Trial and error

• Graphical method

• Long division

When performing synthetic division with imaginary numbers, what is crucial to remember?

• Complex numbers must be handled carefully

• Imaginary numbers can be ignored

• Imaginary numbers should be treated as real numbers

• Imaginary numbers are not part of the solution

What is the relationship between a quotient obtained from synthetic division and the original polynomial?

• The quotient is a factor of the polynomial

• The quotient is unrelated

• The quotient is the remainder

• The quotient is the derivative

What must be included when dealing with complex zeros?

• Only the imaginary part

• The derivatives

• Only the real part

• The conjugates

What is the next step after finding a factor using synthetic division?

• Divide the factor by the polynomial

• Multiply the factor by the polynomial

• Set the factor equal to zero to find remaining zeros

• Ignore the factor

How can you verify if a complex number is a zero of a polynomial?

• By checking if the quotient is zero

• By checking if the remainder is zero

• By checking if the polynomial is undefined

• By checking if the remainder is non-zero

What is the final step in finding all zeros of a polynomial using synthetic division?

• Ignoring the imaginary zeros

• Using synthetic division with the conjugate

• Graphing the polynomial

• Performing long division