The LCM of `(x+2)^(2)(x-2) and (x^(2)-4x-12)` is :

Options

A. `(x+2)(x-2)^(2)`
B. `(x-2)(x+2)(x-6)`
C. `(x-2)(x+2)`
D. `(x-2)(x-6)(x+2)^(2)`

Answer

To find the LCM of the expressions \((x+2)^{2}(x-2)\) and \(x^{2}-4x-12\), we will follow these steps:

### Step 1: Factor the second expression
The second expression is \(x^{2}-4x-12\). We can factor this quadratic expression.

1. **Identify the factors of -12 that add up to -4.** The factors are -6 and +2.
2. **Rewrite the expression:**
\[ x^{2}-4x-12 = (x-6)(x+2) \]