Cubic Equation Factorization Concepts

The video tutorial demonstrates how to solve a cubic equation using factorization. It begins by testing integer roots to find one that satisfies the equation. Once a root is found, the corresponding factor is identified. The tutorial then shows how to form a quadratic equation from the cubic equation's coefficients and solve it to find the remaining factors. Finally, the real solutions of the cubic equation are determined. The video concludes with acknowledgments and a call to action for viewers to subscribe.

What is the first step in solving a cubic equation by factorization?

• Use the quadratic formula

• Graph the equation

• Test integer values to find a root

• Find the derivative of the equation

Which integer was first tested to see if it is a root of the cubic equation?

• 0

• -1

• 2

• 1

What was the result when testing x = 1 as a root of the cubic equation?

• It was a repeated root

• It did not satisfy the equation

• It satisfied the equation

• It was a complex root

Which integer was found to be a root of the cubic equation?

• 3

• -1

• 0

• 2

What factor corresponds to the root x = -1?

• x - 2

• x + 2

• x + 1

• x - 1

What is the next step after finding one factor of the cubic equation?

• Form a quadratic equation

• Use the quadratic formula

• Solve the equation graphically

• Test more integer roots

What are the coefficients of the quadratic equation formed?

• 1, 2, -5

• 1, 1, -6

• 2, -5, -6

• 1, -2, 3

Which two numbers multiply to -6 and add to 1 in the quadratic equation?

• 2 and -3

• -2 and 3

• 1 and -6

• -1 and 6

What are the remaining factors of the cubic equation?

• x - 1 and x + 2

• x + 2 and x - 3

• x - 2 and x + 3

• x + 1 and x - 3

What are the real solutions of the cubic equation?

• -1, 2, -3

• 1, -2, 3

• 1, 2, -3

• -1, -2, 3