(x%2B6).jpeg "(x-4)(x+6)")
Factoring and Solving (x-4)(x+6) = 0
This expression represents the factored form of a quadratic equation. Let's break down what it means and how to solve it.
Understanding Factored Form
The expression (x-4)(x+6) is a product of two binomials. Each binomial represents a linear equation:
- (x-4): This represents a line with a slope of 1 and a y-intercept of -4.
- (x+6): This represents a line with a slope of 1 and a y-intercept of 6.
When these two binomials are multiplied, they create a quadratic expression.
Finding the Roots
The equation (x-4)(x+6) = 0 is asking: "For what values of x does the product of these two binomials equal zero?".
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.
Therefore, to solve for x, we set each binomial equal to zero and solve:
- x - 4 = 0 => x = 4
- x + 6 = 0 => x = -6
Conclusion
The solutions to the equation (x-4)(x+6) = 0 are x = 4 and x = -6. These values represent the roots or x-intercepts of the quadratic equation formed by expanding (x-4)(x+6).
In other words, the graph of the quadratic equation would intersect the x-axis at the points x = 4 and x = -6.