Understanding Zeros of Polynomials

The video tutorial explains how to find the zeros of a polynomial by examining its graph and factoring. It covers several examples, including factoring x^2 + x - 6 and x^2 - 9x + 20, and demonstrates how to use known zeros to determine polynomial factors. The tutorial emphasizes the importance of understanding zeros to reconstruct the original polynomial equation.

What is the significance of the sign of the linear term in the polynomial x^2 + x - 6?

• It determines the degree of the polynomial.

• It helps in deciding the signs of the factors.

• It shows the leading coefficient.

• It indicates the number of zeros.

Which pair of numbers is used to factor the polynomial x^2 + x - 6?

• (3, 2)

• (2, 3)

• (1, 6)

• (6, 1)

In the polynomial x^2 - 9x + 20, which pair of numbers is used to factor it?

• (1, 20)

• (5, 4)

• (2, 10)

• (4, 5)

What is the result of factoring x^2 - 9x + 20?

• (x + 5)(x - 4)

• (x - 5)(x + 4)

• (x + 4)(x + 5)

• (x - 4)(x - 5)

How can knowing the zeros of a polynomial help in reconstructing the original equation?

• It allows for the identification of the factors.

• It helps in determining the leading coefficient.

• It provides the degree of the polynomial.

• It shows the constant term.

If a polynomial has zeros at -6 and -2, what are its factors?

• (x + 6)(x + 2)

• (x - 6)(x - 2)

• (x - 6)(x + 2)

• (x + 6)(x - 2)

What is the factored form of a polynomial with zeros at -8 and 10?

• (x + 8)(x - 10)

• (x - 8)(x + 10)

• (x - 8)(x - 10)

• (x + 8)(x + 10)

How does the product of the factors relate to the original polynomial?

• It is double the original polynomial.

• It is unrelated to the original polynomial.

• It is half of the original polynomial.

• It equals the original polynomial.

What is the relationship between the zeros and the y-values on the graph?

• Zeros are where y-values are maximum.

• Zeros are where y-values are minimum.

• Zeros are where y-values are zero.

• Zeros are where y-values are undefined.

Why is it useful to know the zeros of a polynomial?

• To identify the polynomial's constant term.

• To reconstruct the polynomial's equation.

• To find the polynomial's leading coefficient.

• To determine the polynomial's degree.