(x^2+2x-8)(x-6)=0

2 min read Jun 17, 2024

Solving the Equation (x^2+2x-8)(x-6)=0

This equation represents a polynomial equation that can be solved using factorization and the Zero Product Property. Let's break down the steps:

1. Factor the Quadratic Expression

First, we need to factor the quadratic expression x² + 2x - 8.

We look for two numbers that multiply to -8 and add up to 2. These numbers are 4 and -2.
Therefore, we can rewrite the quadratic expression as (x + 4)(x - 2).

Now our equation becomes: (x + 4)(x - 2)(x - 6) = 0

2. Apply the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation, we get three possible scenarios:

x + 4 = 0
x - 2 = 0
x - 6 = 0

3. Solve for x

Solving each of these equations, we find:

x = -4
x = 2
x = 6

Conclusion

Therefore, the solutions to the equation (x² + 2x - 8)(x - 6) = 0 are x = -4, x = 2, and x = 6. These are the roots or zeros of the polynomial.