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(x+4)(x-8)=0

2 min read Jun 16, 2024
(x+4)(x-8)=0

Solving the Equation (x+4)(x-8)=0

This equation is a simple quadratic equation in factored form. We can use the Zero Product Property to solve it. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Here's how to solve it:

  1. Set each factor equal to zero:

    • x + 4 = 0
    • x - 8 = 0

  2. Solve for x in each equation:

    • x = -4
    • x = 8

Therefore, the solutions to the equation (x+4)(x-8)=0 are x = -4 and x = 8.

Understanding the Zero Product Property

The Zero Product Property is a fundamental concept in algebra. It allows us to easily solve equations that are in factored form. By setting each factor to zero, we isolate the values of x that make the entire equation true.

Visual Representation

We can visualize these solutions on a number line. The solutions represent the x-intercepts of the quadratic function represented by the equation.

[Insert Image of number line with points at -4 and 8]

Conclusion

Solving (x+4)(x-8)=0 using the Zero Product Property is a straightforward process. Understanding this property is essential for solving many quadratic equations and other algebraic problems.

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