Solving the Cubic Equation: (x+2)(x+4)(x1) = 0
This equation presents a cubic polynomial, meaning it has a highest power of 3. To find the solutions, we utilize the Zero Product Property: if the product of several factors equals zero, then at least one of the factors must be zero.
Applying the Zero Product Property

Identify the factors: We have three factors: (x+2), (x+4), and (x1).

Set each factor equal to zero:
 x + 2 = 0
 x + 4 = 0
 x  1 = 0

Solve for x in each equation:
 x = 2
 x = 4
 x = 1
Solutions
Therefore, the solutions to the equation (x+2)(x+4)(x1) = 0 are x = 2, x = 4, and x = 1. These are the roots or zeros of the cubic polynomial.
Graphical Representation
The solutions of a polynomial equation correspond to the points where the graph of the polynomial intersects the xaxis. A cubic polynomial like this one will have at most three xintercepts, which we have identified as (2, 0), (4, 0), and (1, 0).
Key Takeaways
 The Zero Product Property is a powerful tool for solving polynomial equations.
 Cubic equations can have up to three solutions.
 The solutions of a polynomial equation represent the points where the graph intersects the xaxis.