(x-7)%3D0-zero-product-property.jpeg "(x+13)(x-7)=0 Zero Product Property")
Solving Equations Using the Zero Product Property
The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero. This property is extremely useful when solving equations that are in factored form.
Let's take a look at the equation:
(x + 13)(x - 7) = 0
This equation is already factored, meaning we have two factors: (x + 13) and (x - 7). To satisfy the Zero Product Property, at least one of these factors must equal zero. Therefore, we can set each factor equal to zero and solve for x:
x + 13 = 0 or x - 7 = 0
Solving for x in each equation:
- x + 13 = 0
- Subtract 13 from both sides: x = -13
- x - 7 = 0
- Add 7 to both sides: x = 7
Therefore, the solutions to the equation (x + 13)(x - 7) = 0 are x = -13 and x = 7.
Understanding the Zero Product Property
The Zero Product Property is a powerful tool for solving equations. It allows us to break down complex equations into simpler ones by setting each factor equal to zero. This is especially helpful when dealing with equations that are in factored form.
Key Points
- The Zero Product Property only works when the product of the factors equals zero.
- For each factor, set it equal to zero and solve for the variable.
- The solutions to the equation are the values of the variable that make each factor equal to zero.