(x+2)(x+4)(x-1) 0

Jasonbradley

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Jun 16, 2024

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Solving the Cubic Equation: (x+2)(x+4)(x-1) = 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

1. Identify the factors: We have three factors: (x+2), (x+4), and (x-1).

2. Set each factor equal to zero:

   • x + 2 = 0
   • x + 4 = 0
   • x - 1 = 0

3. Solve for x in each equation:

   • x = -2
   • x = -4
   • x = 1

Solutions

Therefore, the solutions to the equation (x+2)(x+4)(x-1) = 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 x-axis. A cubic polynomial like this one will have at most three x-intercepts, 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 x-axis.