Use Synthetic Division to Find the Remaining Zeros Given One Imaginary Zero

The video tutorial explains synthetic division, focusing on proving zeros of polynomials. It covers using synthetic division with complex numbers, factoring polynomials, and applying the zero product property to find zeros. The tutorial emphasizes understanding complex conjugates and their role in division.

What is one method to verify if a number is a zero of a polynomial?

• Graphing the polynomial

• Performing long division

• Using the quadratic formula

• Applying the remainder theorem

When performing synthetic division with complex numbers, what should you be cautious about?

• Avoiding multiplication

• Using only real numbers

• Leaving extra space between coefficients

• Ignoring the imaginary part

What is the result of multiplying 5i by 10i?

• -50i

• -50

• 50

• 50i

Why is it important to include the conjugate when dealing with complex numbers?

• To account for all possible zeros

• To simplify the polynomial

• To ensure all real roots are found

• To avoid imaginary numbers

What is the first step in finding the zeros of a polynomial using the zero product property?

• Divide by the leading coefficient

• Graph the polynomial

• Set the polynomial equal to zero

• Multiply all factors