(x%2B7).jpeg "(x-1)(x+7)")
Factoring and Solving (x-1)(x+7) = 0
This expression represents a product of two binomials: (x-1) and (x+7). We can analyze this expression in a few ways:
1. Expanding the Expression
We can distribute the terms to get a standard quadratic equation:
(x-1)(x+7) = x(x+7) - 1(x+7) = x² + 7x - x - 7 = x² + 6x - 7
2. Finding the Roots (Solving for x)
When the product of two factors equals zero, at least one of the factors must be zero. This is known as the Zero Product Property.
Therefore, to find the solutions for:
(x-1)(x+7) = 0
We set each factor equal to zero:
- x - 1 = 0 => x = 1
- x + 7 = 0 => x = -7
These are the solutions or roots of the equation.
3. Graphing the Equation
The expression (x-1)(x+7) represents a parabola. Its roots, x = 1 and x = -7, are the points where the parabola intersects the x-axis.
Key Points
- The expression (x-1)(x+7) is a factored form of a quadratic equation.
- The Zero Product Property is a valuable tool for solving equations where factors are multiplied.
- The roots of the equation represent the x-intercepts of the parabola.