Algebra II Recipe: Factoring and Solving Polynomial Equations

A. Factoring the Sum of Two Cubes

1. It always factors into: (a + b) (a² - ab + b²)
2. The "a" and "b" represent terms.
   • "a" is the cube root of the first term.
   • "b" is the cube root of the xecond term.

B. Factoring the Difference of Two Cubes

1. It always factors into: (a - b) (a² + ab + b²)
2. The "a" and "b" represent terms.
   • "a" is the cube root of the first term.
   • "b" is the cube root of the xecond term.

C. Solving Polynomial Equations by Factoring

1. Set all terms equal to zero.
2. Factor the polynomial completely.
3. Set each factor that has a variable equal to zero.
4. Solve each equation.
5. The values you get after solving are the solutions.

Practice Problems