(x-5)(x-7)-0.jpeg "(x+3)(x-5)(x-7) 0")
Solving the Equation (x+3)(x-5)(x-7) = 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)(x-5)(x-7) = 0 are x = -3, x = 5, and x = 7.
These solutions represent the x-intercepts of the graph of the cubic function defined by the equation. In other words, the graph crosses the x-axis at these points.