(x+3)(x-2)(x+1)(x-1)=0

Jasonbradley

2 min read

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Jun 16, 2024

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Solving the Equation (x+3)(x-2)(x+1)(x-1)=0

This equation involves the product of four factors that equal zero. The fundamental principle we use to solve this is the 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 break down the solution:

1. Set each factor equal to zero:

• x + 3 = 0
• x - 2 = 0
• x + 1 = 0
• x - 1 = 0

2. Solve each equation for x:

• x = -3
• x = 2
• x = -1
• x = 1

Therefore, the solutions to the equation (x+3)(x-2)(x+1)(x-1) = 0 are x = -3, x = 2, x = -1, and x = 1.

Important Note: This equation has four distinct solutions because it's a fourth-degree polynomial. The number of solutions to a polynomial equation is generally equal to its highest degree.

Graphical Interpretation:

The graph of the function y = (x+3)(x-2)(x+1)(x-1) will intersect the x-axis at the points (-3, 0), (2, 0), (-1, 0), and (1, 0). These points correspond to the solutions we found.

This equation demonstrates how the Zero Product Property helps us solve equations by breaking down complex expressions into simpler ones.