Understanding Cubic Equations and Their Factors

The video tutorial explains how to determine the factors of a cubic equation given its roots. It starts by identifying the roots of the equation as -5, 0, and 3, and explains that each root corresponds to a factor of the form (x - root). The tutorial then simplifies the expression to show that the product of these factors equals zero, confirming the roots. Finally, it verifies the solution by checking that each root satisfies the equation, concluding that x + 5 is a factor of the cubic expression.

What are the roots of the given cubic equation?

• -3, 0, and 5

• 0, 1, and 5

• 1, 2, and 3

• -5, 0, and 3

Which of the following represents a factor of the cubic equation if x = -5 is a root?

• x - 3

• x + 3

• x - 5

• x + 5

What is the simplified form of the expression derived from the roots?

• x(x - 5)(x + 3)

• x(x + 5)(x - 3)

• x(x + 3)(x - 5)

• x(x - 3)(x + 5)

How is the expression x(x + 5)(x - 3) related to the roots of the equation?

• It is the factorized form of the equation.

• It is unrelated to the roots.

• It is the product of the roots.

• It is the sum of the roots.

Which factor is confirmed to be part of the cubic expression?

• x - 5

• x + 3

• x + 5

• x - 3