(x-6)(x+4)

Jasonbradley

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Jun 17, 2024

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Factoring and Solving (x - 6)(x + 4) = 0

The expression (x - 6)(x + 4) represents a factored quadratic equation. Let's explore what this means and how to solve it.

Understanding the Factored Form

The factored form of a quadratic equation tells us the values of x that make the equation equal to zero. Here's how it works:

• Zero Product Property: If the product of two or more factors is zero, at least one of the factors must be zero.
• Applying to our expression: For (x - 6)(x + 4) to equal zero, either (x - 6) must be zero or (x + 4) must be zero.

Solving for x

1. Set each factor equal to zero:

   • x - 6 = 0
   • x + 4 = 0

2. Solve for x in each equation:

   • x = 6
   • x = -4

Solutions

Therefore, the solutions to the equation (x - 6)(x + 4) = 0 are x = 6 and x = -4.

Conclusion

By understanding the zero product property and factoring, we can easily solve quadratic equations in factored form. These solutions represent the x-intercepts of the parabola represented by the original quadratic equation.