(x+2)(x+3)=0 Answer

Jasonbradley

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Jun 16, 2024

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Solving the Equation (x+2)(x+3) = 0

This equation represents a quadratic equation in factored form. To find the solutions (also called roots or zeros) of this equation, we can use the Zero Product Property:

Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.

Let's apply this property to our equation:

1. Set each factor equal to zero:

   • x + 2 = 0
   • x + 3 = 0

2. Solve for x in each equation:

   • x = -2
   • x = -3

Therefore, the solutions to the equation (x+2)(x+3) = 0 are x = -2 and x = -3.

Explanation:

The equation (x+2)(x+3) = 0 implies that the product of the expressions (x+2) and (x+3) is zero. This can only happen if either (x+2) is zero or (x+3) is zero. By setting each factor equal to zero, we find the values of x that satisfy this condition.

Graphical Representation:

The solutions of this equation correspond to the x-intercepts of the parabola represented by the equation y = (x+2)(x+3). The graph will intersect the x-axis at x = -2 and x = -3.

In summary:

The equation (x+2)(x+3) = 0 is easily solved using the Zero Product Property. The solutions are x = -2 and x = -3, representing the points where the graph of the equation intersects the x-axis.