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(x+5)(x-8) 0

2 min read Jun 17, 2024
(x+5)(x-8) 0

Solving the Equation (x + 5)(x - 8) = 0

This equation represents a quadratic expression set equal to zero. To solve for x, we can use the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve the equation:

  1. Identify the factors: We have two factors: (x + 5) and (x - 8).

  2. Set each factor equal to zero:

    • x + 5 = 0
    • x - 8 = 0

  3. Solve for x in each equation:

    • x = -5
    • x = 8

Therefore, the solutions to the equation (x + 5)(x - 8) = 0 are x = -5 and x = 8.

Understanding the Solution

These solutions represent the x-intercepts of the parabola defined by the quadratic expression (x + 5)(x - 8). In other words, the graph of the parabola crosses the x-axis at the points (-5, 0) and (8, 0).

In summary:

  • The Zero Product Property is a powerful tool for solving quadratic equations in factored form.
  • The solutions to the equation (x + 5)(x - 8) = 0 are x = -5 and x = 8.
  • These solutions represent the x-intercepts of the parabola defined by the expression.

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