(x-8)(x%2B5)-0.jpeg "(x+2)(x-8)(x+5) 0")
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.