Understanding Zeros of Polynomials

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.