Solving the Cubic Equation: (x + 3)(x  2)(x  4) = 0
This equation represents a cubic function, meaning it has a highest power of x equal to 3. To solve for the values of x that make the equation true, we can use the Zero Product Property.
The Zero Product Property
The Zero Product Property states that 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 the Property to our Equation
In our equation, we have three factors: (x + 3), (x  2), and (x  4). To make the product equal to zero, at least one of these factors must equal zero.
Therefore, we set each factor equal to zero and solve for x:

x + 3 = 0
 Subtract 3 from both sides: x = 3

x  2 = 0
 Add 2 to both sides: x = 2

x  4 = 0
 Add 4 to both sides: x = 4
Solutions
The solutions to the equation (x + 3)(x  2)(x  4) = 0 are:
 x = 3
 x = 2
 x = 4
These solutions represent the xintercepts of the cubic function. In other words, the graph of this function will cross the xaxis at these points.