(x+2)(x-8)(x+5) 0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+2)(x-8)(x+5) = 0

This equation represents a cubic polynomial. To solve for the values of x that satisfy the equation, we can utilize the Zero Product Property:

Zero Product Property: If the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Applying this to our equation:

• (x+2)(x-8)(x+5) = 0

This means that one or more of the following must be true:

• x + 2 = 0
• x - 8 = 0
• x + 5 = 0

Solving each of these linear equations, we get:

• x = -2
• x = 8
• x = -5

Therefore, the solutions to the equation (x+2)(x-8)(x+5) = 0 are x = -2, x = 8, and x = -5.

Understanding the Concept

This equation represents a cubic function, which is a function with a highest power of 3. The solutions we found are the roots or x-intercepts of this function. These are the points where the graph of the function crosses the x-axis.

In other words, the solutions to the equation are the values of x where the function equals zero.