Solving the Quadratic Equation (x+4)(x1)=0
This article will guide you through the process of solving the quadratic equation (x+4)(x1)=0. We will explore the concept of the zero product property and use it to find the solutions for x.
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 equal to zero. This property is crucial for solving equations in factored form.
Applying the Zero Product Property
In the equation (x+4)(x1)=0, we have two factors: (x+4) and (x1). To satisfy the zero product property, at least one of these factors must be equal to zero.
Therefore, we can set up two equations:
 x+4 = 0
 x1 = 0
Solving for x
Now we solve each equation for x:

x+4 = 0 Subtract 4 from both sides: x = 4

x1 = 0 Add 1 to both sides: x = 1
Solutions
Therefore, the solutions to the quadratic equation (x+4)(x1)=0 are x = 4 and x = 1.
Conclusion
By utilizing the zero product property, we efficiently solved the quadratic equation (x+4)(x1)=0. We found two distinct solutions for x, which are 4 and 1. This method provides a simple and effective approach to solving factored quadratic equations.