Solving Cubic Equations by Factor By Grouping

This video tutorial explains how to solve cubic equations using the factor by grouping technique. It provides two examples: the first involves solving x^3 + 2x^2 - 9x - 18 = 0, and the second involves solving x^3 - x^2 - 3x + 15 = 0. The tutorial demonstrates factoring by grouping, identifying common binomial factors, and using the zero product property to find solutions. The first example results in three real rational solutions, while the second example yields one real rational solution and two real irrational solutions.

What technique is recommended for solving cubic equations with four terms?

• Factor by Grouping

• Synthetic Division

• Quadratic Formula

• Completing the Square

In the first example, what is the greatest common factor of x^3 + 2x^2?

• 2x^2

• 2x

• x^2

• x

Why do we factor out -9 instead of 9 from -9x - 18?

• To get a positive binomial factor

• To get a common binomial factor

• To simplify the equation

• To make the equation easier to solve

What are the solutions to the equation x^3 + 2x^2 - 9x - 18 = 0?

• x = -2, x = 3, x = -3

• x = 2, x = 3, x = -3

• x = -2, x = -3, x = 3

• x = 2, x = -3, x = 3

In the second example, what is the greatest common factor of x^3 - x^2?

• 1

• x

• x^2

• x^3

Why do we factor out -3 instead of 3 from -3x + 15?

• To get a positive binomial factor

• To make the equation easier to solve

• To simplify the equation

• To get a common binomial factor

What is the next step after factoring out the common binomial factor in the second example?

• Combine like terms

• Use the zero product property

• Use the quadratic formula

• Solve the equation directly

What are the solutions to the equation x^3 - x^2 - 3x + 15 = 0?

• x = -5, x = ±√2

• x = -5, x = ±√3

• x = 5, x = ±√2

• x = 5, x = ±√3

What property is used to solve the equation after factoring?

• Associative Property

• Zero Product Property

• Commutative Property

• Distributive Property

What type of solutions are x = ±√3?

• Complex Solutions

• Real Rational Solutions

• Imaginary Solutions

• Real Irrational Solutions