Polynomial Roots and Factors

The video tutorial explains how to analyze polynomial roots using factored form. It covers identifying roots from a graph, determining the corresponding factors, and understanding the role of sign changes in determining the exponent of each factor. The tutorial provides examples with roots at x = -4, x = -3/2, x = 1, x = -3, and x = 2, illustrating how to choose the correct polynomial equation based on these roots.

What is the primary use of expressing a polynomial in factored form?

• To find the roots of the polynomial

• To determine the degree of the polynomial

• To calculate the polynomial's derivative

• To simplify the polynomial

If a polynomial has a root at x = -4, what factor should be present?

• x - 2

• x - 4

• x + 4

• x + 2

What does a sign change around a root indicate about the exponent of the factor?

• The exponent is zero

• The exponent is negative

• The exponent is even

• The exponent is odd

For the root at x = -3/2, which factor is correct?

• x + 3/2

• x - 3/2

• 2x + 3

• 2x - 3

What exponent is expected for the factor corresponding to the root at x = -3/2?

• Negative

• Zero

• Odd

• Even

Which factor corresponds to the root at x = 1?

• x + 1

• x - 1

• x + 2

• x - 2

What type of exponent is expected for the factor at x = 1, given no sign change?

• Negative

• Zero

• Even

• Odd

In the new example, what factor is expected for the root at x = -3?

• x + 2

• x + 3

• x - 3

• x - 2

What type of exponent is expected for the factor at x = -3?

• Even

• Odd

• Zero

• Negative

For the root at x = 2, what factor should be present?

• x - 3

• x + 3

• x - 2

• x + 2