Master how to find all of the zeros of a polynomial when given two complex zerosgiven c

The video tutorial explains how to find all zeros of a polynomial when given one complex zero. It covers the use of synthetic division to find other factors, the role of complex conjugates, and alternative methods for finding zeros. The tutorial also demonstrates multiplying and dividing factors to simplify the polynomial and find real zeros.

What is the first step in finding another factor of a polynomial when given a complex zero?

• Use the quadratic formula

• Apply synthetic division

• Use the remainder theorem

• Find the derivative

When adding complex numbers during synthetic division, what should you remember?

• Ignore the imaginary parts

• Subtract the imaginary parts

• Add the real and imaginary parts separately

• Multiply the real parts only

Why is it important to check for a zero remainder in synthetic division?

• To determine the leading coefficient

• To find the degree of the polynomial

• To identify the constant term

• To confirm the zero is correct

What is the benefit of using the complex conjugate when finding zeros?

• It simplifies the polynomial

• It provides additional real zeros

• It reduces the polynomial's degree

• It ensures all zeros are found

How can you write a polynomial in factored form using its zeros?

• By setting each zero equal to zero

• By adding the zeros to the polynomial

• By multiplying the zeros together

• By using the zeros to form linear factors

What is the difference of squares used for in this context?

• To find the derivative of a polynomial

• To simplify complex numbers

• To multiply factors and find another factor

• To add complex conjugates

What is an alternative method to synthetic division for finding zeros?

• Using the quadratic formula

• Using the difference of squares

• Using polynomial long division

• Using the binomial theorem