(x-4)(x+3)(-x-8)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-4)(x+3)(-x-8) = 0

This equation represents a cubic function, which means it has a maximum of three solutions or roots. To find these roots, we can utilize the Zero Product Property:

Zero Product Property: 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:

(x-4)(x+3)(-x-8) = 0

We have three factors:

1. (x-4)
2. (x+3)
3. (-x-8)

For the product to equal zero, at least one of these factors must be zero. Let's solve for each case:

Case 1: (x-4) = 0

• Solving for x, we get: x = 4

Case 2: (x+3) = 0

• Solving for x, we get: x = -3

Case 3: (-x-8) = 0

• Solving for x, we get: x = -8

Therefore, the solutions to the equation (x-4)(x+3)(-x-8) = 0 are x = 4, x = -3, and x = -8.

Understanding the Solution:

These solutions represent the x-intercepts of the graph of the cubic function represented by the equation. In other words, the graph crosses the x-axis at the points (4, 0), (-3, 0), and (-8, 0).

In Summary:

By using the Zero Product Property, we successfully found the three solutions (roots) of the equation (x-4)(x+3)(-x-8) = 0, which are x = 4, x = -3, and x = -8. These solutions also represent the x-intercepts of the corresponding cubic function.