(x-8)(x^3+8)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-8)(x³+8) = 0

This equation involves a product of two factors that equals zero. The key principle to solving this is the Zero Product Property, which states that 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. Identify the Factors

We have two factors in the equation:

• (x-8)
• (x³+8)

2. Apply the Zero Product Property

For the product of the two factors to be zero, at least one of them must be equal to zero. Therefore, we have two possibilities:

• (x-8) = 0
• (x³+8) = 0

3. Solve for x in Each Equation

• Solving (x-8) = 0

  • Add 8 to both sides:
    • x = 8

• Solving (x³+8) = 0

  • Subtract 8 from both sides:
    • x³ = -8
  • Take the cube root of both sides:
    • x = -2

4. Solutions

The solutions to the equation (x-8)(x³+8) = 0 are:

• x = 8
• x = -2

Therefore, the equation has two solutions: x = 8 and x = -2.