Solving the Equation (x+3)(x5)(x7) = 0
This equation represents a cubic polynomial, and to find its solutions (or roots), we need to find the values of x that make the equation true. The key to solving this type of equation is understanding 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, we have three factors:
 (x + 3)
 (x  5)
 (x  7)
For the product of these factors to equal zero, at least one of them must be zero. Therefore, we can set each factor equal to zero and solve for x:

x + 3 = 0 Subtracting 3 from both sides gives us: x = 3

x  5 = 0 Adding 5 to both sides gives us: x = 5

x  7 = 0 Adding 7 to both sides gives us: x = 7
Therefore, the solutions to the equation (x+3)(x5)(x7) = 0 are x = 3, x = 5, and x = 7.
These solutions represent the xintercepts of the graph of the cubic function defined by the equation. In other words, the graph crosses the xaxis at these points.