Solving Cubic Equations by Factor By Grouping

Factor by Grouping

Synthetic Division

Quadratic Formula

Completing the Square

2x^2

2x

x^2

x

To get a positive binomial factor

To get a common binomial factor

To simplify the equation

To make the equation easier to solve

x = -2, x = 3, x = -3

x = 2, x = 3, x = -3

x = -2, x = -3, x = 3

x = 2, x = -3, x = 3

1

x

x^2

x^3

To get a positive binomial factor

To make the equation easier to solve

To simplify the equation

To get a common binomial factor

Combine like terms

Use the zero product property

Use the quadratic formula

Solve the equation directly

x = -5, x = ±√2

x = -5, x = ±√3

x = 5, x = ±√2

x = 5, x = ±√3

Associative Property

Zero Product Property

Commutative Property

Distributive Property

Complex Solutions

Real Rational Solutions

Imaginary Solutions

Real Irrational Solutions