Given One Zero or Factor Find the Remaining Zeros

The video tutorial explains how to find the zeros of a polynomial, specifically focusing on a polynomial with irrational zeros. It covers the use of complex conjugates, setting zeros as factors, and multiplying them using FOIL and the difference of squares. The tutorial also demonstrates using long division to find remaining zeros, ensuring a comprehensive understanding of polynomial division and factorization.

What is the polynomial F(x) given in the video?

• F(x) = x^3 - x^2 - 13x - 3

• F(x) = x^3 - x^2 + 13x - 3

• F(x) = x^3 + x^2 - 13x + 3

• F(x) = x^3 + x^2 + 13x + 3

If 2 - sqrt(5) is a zero of the polynomial, what is its complex conjugate?

• -2 - sqrt(5)

• -2 + sqrt(5)

• 2 - sqrt(5)

• 2 + sqrt(5)

What method is used to multiply the factors (x - 2 - sqrt(5)) and (x - 2 + sqrt(5))?

• Difference of squares

• Sum of cubes

• Product of sums

• Quadratic formula

What is the quadratic factor derived from the zeros 2 - sqrt(5) and 2 + sqrt(5)?

• x^2 + 4x + 1

• x^2 + 4x - 1

• x^2 - 4x - 1

• x^2 - 4x + 1

Why is long division used instead of synthetic division in this problem?

• The zeros are complex numbers

• The divisor is not a binomial

• The polynomial is already factored

• The polynomial is not cubic

What is the final zero found after performing long division?

• x = 1

• x = 3

• x = -3

• x = 0

How many total zeros does the polynomial have?

• Two

• Three

• One

• Four