(x%2B2)(x-9)-0.jpeg "(x+11)(x+2)(x-9) 0")
Solving the Equation: (x+11)(x+2)(x-9) = 0
This equation represents a cubic polynomial, and we are tasked with finding the values of x that make the equation true. The most straightforward way to solve this is by using the Zero Product Property.
The Zero Product Property
This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero. In our case, we have three factors:
- (x + 11)
- (x + 2)
- (x - 9)
For the entire product to be zero, one or more of these factors must be zero. Therefore, we can solve for x by setting each factor equal to zero and solving:
1. x + 11 = 0 Subtracting 11 from both sides gives us: x = -11
2. x + 2 = 0 Subtracting 2 from both sides gives us: x = -2
3. x - 9 = 0 Adding 9 to both sides gives us: x = 9
Solution
Therefore, the solutions to the equation (x+11)(x+2)(x-9) = 0 are x = -11, x = -2, and x = 9. These are the values of x that will make the equation true.