Given a Complex Zero Find the Remaining Zeros Using Synthetic Division

The video tutorial explains how to find zeros of a polynomial using synthetic division, even with imaginary numbers. It covers the process of identifying factors, performing synthetic division, and finding all zeros of a polynomial. The tutorial also discusses polynomial factorization and concludes with a brief mention of alternative methods.

What is the first step in finding the remaining factors of a polynomial when given a zero?

• Use long division

• Graph the polynomial

• Perform synthetic division

• Use the quadratic formula

How do you handle imaginary numbers during synthetic division?

• Ignore them

• Treat them like real numbers

• Convert them to real numbers

• Use a different method

What is the result of multiplying 2 + 4i by -4i in synthetic division?

• Negative 16

• Zero

• Positive 16

• Negative 8

What is the purpose of finding the quotient in synthetic division?

• To identify the leading coefficient

• To find the remainder

• To simplify the polynomial

• To determine the degree of the polynomial

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

• Divide by the leading coefficient

• Multiply all factors

• Add all coefficients

• Set each factor equal to zero

Which of the following is a zero of the polynomial discussed in the video?

• 6

• 2

• 3

• 5

What does linear factorization involve?

• Writing the polynomial as a sum of terms

• Finding the derivative of the polynomial

• Writing the polynomial as a product of linear factors

• Integrating the polynomial