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Solving the Equation: (x+1)(x-4) = 0
This equation represents a simple quadratic equation in factored form. Solving for x involves understanding the concept of the Zero Product Property.
Understanding 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 zero.
In our equation, we have two factors: (x+1) and (x-4). To make the product equal to zero, at least one of these factors must be equal to zero.
Solving for x
Let's set each factor equal to zero and solve:
1. x + 1 = 0 Subtracting 1 from both sides gives us: x = -1
2. x - 4 = 0 Adding 4 to both sides gives us: x = 4
Conclusion
Therefore, the solutions to the equation (x+1)(x-4) = 0 are x = -1 and x = 4.
These solutions represent the points where the graph of the quadratic function y = (x+1)(x-4) intersects the x-axis.