(x%2B2)(x-8)-0.jpeg "(x+5)(x+2)(x-8) 0")
Solving the Equation (x+5)(x+2)(x-8) = 0
This equation involves a product of three factors that equals zero. To find the solutions, 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.
Let's apply this to our equation:
(x + 5)(x + 2)(x - 8) = 0
This means one or more of the following must be true:
- x + 5 = 0
- x + 2 = 0
- x - 8 = 0
Now, we can solve each of these simple equations:
- x + 5 = 0 => x = -5
- x + 2 = 0 => x = -2
- x - 8 = 0 => x = 8
Therefore, the solutions to the equation (x+5)(x+2)(x-8) = 0 are x = -5, x = -2, and x = 8.
Understanding the Solutions
These solutions represent the x-intercepts of the graph of the function y = (x+5)(x+2)(x-8). This means that the graph crosses the x-axis at the points (-5, 0), (-2, 0), and (8, 0).
Conclusion
By applying the Zero Product Property, we have successfully solved the equation (x+5)(x+2)(x-8) = 0. We found three distinct solutions, which represent the x-intercepts of the corresponding function. This method can be applied to solve similar equations involving products of factors.