Factoring and Solving Cubic Equations

The video tutorial explains how to find real solutions of a cubic equation using factoring by grouping. It begins with an introduction to the method, followed by a detailed explanation of factoring by grouping. The tutorial then demonstrates how to solve the equation by factoring out common terms and identifying solutions from the factored terms. The final solutions are x equals 2, negative 3, and positive 3.

What method is used in the video to find the real solutions of the cubic equation?

• Quadratic formula

• Completing the square

• Synthetic division

• Factoring by grouping

What is factored out from the first two terms of the cubic equation?

• x

• x squared

• Nine

• x minus 2

What is the result of factoring the expression x squared times x minus 2?

• x cubed plus 2x squared

• x squared minus 2x

• x squared plus 2x

• x cubed minus 2x squared

What is the common factor extracted from the last two terms?

• x

• x squared

• x minus 2

• Nine

What is the expression after factoring out nine from the last two terms?

• 9 times x minus 2

• 9x plus 18

• 9x minus 18

• 9 times x plus 2

What common factor is identified in the expression after factoring?

• Nine

• x minus 2

• x plus 2

• x squared

What is the equation after combining the common factor x minus 2?

• (x minus 2)(x squared minus 2) = 0

• (x minus 2)(x squared plus 2) = 0

• (x minus 2)(x squared minus 9) = 0

• (x minus 2)(x squared plus 9) = 0

How is the expression simplified using the difference of squares?

• By dividing terms

• By expressing as a product of two binomials

• By subtracting terms

• By adding terms

What is the purpose of expressing the factor as a difference of squares?

• To simplify the equation

• To add complexity

• To find the roots

• To eliminate terms

What is one of the solutions for x from the factors?

• x = 0

• x = 1

• x = 2

• x = -1