Finding the Zeros Given One Complex Zeros

The video tutorial explains how to handle complex zeros in polynomials, focusing on using synthetic and long division. It begins by identifying complex zeros and their conjugates, then demonstrates multiplying these conjugates to eliminate imaginary parts. The tutorial proceeds to apply long division to find polynomial factors and zeros, emphasizing the importance of identifying all zeros for polynomial equations.

If 5 + 2i is a zero of a polynomial, what is its conjugate?

• 5 + 2i

• 5 - 2i

• 5 - 3i

• 5 + 3i

What happens when a complex number is multiplied by its conjugate?

• The result is zero

• The real part is eliminated

• The result is a complex number

• The imaginary part is eliminated

What is the polynomial factor for the zero 5 + 2i?

• X + 5 + 2i

• X + 5 - 2i

• X - 5 + 2i

• X - 5 - 2i

What is the result of multiplying (X - 5)^2 and -4i^2?

• X^2 - 10X + 24

• X^2 - 10X + 21

• X^2 - 10X + 29

• X^2 - 10X + 25

In polynomial division, what is the first step when dividing X^3 by X^2?

• Multiply by 10

• Multiply by 3

• Multiply by X^2

• Multiply by X

What is the last remaining factor after completing the polynomial division?

• X - 3

• X + 2

• X + 3

• X - 2

What confirms that a number is a zero of a polynomial?

• The polynomial equals three when evaluated at that number

• The polynomial equals zero when evaluated at that number

• The polynomial equals two when evaluated at that number

• The polynomial equals one when evaluated at that number