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0=(x-3)(x+4)(x^2-4)

2 min read Jun 17, 2024
0=(x-3)(x+4)(x^2-4)

Solving the Equation: 0 = (x-3)(x+4)(x^2-4)

This equation is a polynomial equation that can be solved by factoring and applying the zero product property. Here's how to solve it step by step:

1. Factoring the Equation

  • Recognize the Difference of Squares: The term (x² - 4) is a difference of squares, which can be factored as (x-2)(x+2).
  • Full Factorization: Now we can rewrite the equation as: 0 = (x-3)(x+4)(x-2)(x+2)

2. Applying the Zero Product Property

The zero product property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation, we have four factors:

  • x-3 = 0
  • x+4 = 0
  • x-2 = 0
  • x+2 = 0

3. Solving for x

Solving each of these equations for x gives us the following solutions:

  • x = 3
  • x = -4
  • x = 2
  • x = -2

Conclusion

Therefore, the solutions to the equation 0 = (x-3)(x+4)(x² - 4) are x = 3, x = -4, x = 2, and x = -2.

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