Factor the following trinomial \[ x^{2}-4 x-32 \] Select the correct choce below and, il necessary, fill in the answer box to complete your choice. A. \( x^{2}-4 x-32= \) (Type your answer in factored form.) B. The polynomial is prime.

1. We need to factor the trinomial \[ x^{2}-4x-32. \] 2. Look for two numbers \( m \) and \( n \) such that \[ m \cdot n = -32 \quad \text{and} \quad m+n = -4. \] 3. Testing possible pairs, we find that \( 4 \) and \( -8 \) work because \[ 4 \cdot (-8) = -32 \quad \text{and} \quad 4+(-8)=-4. \] 4. Rewrite the trinomial by splitting the middle term: \[ x^{2}-4x-32 = x^{2}+4x-8x-32. \] 5. Factor by grouping: \[ (x^{2}+4x) + (-8x-32). \] 6. Factor out the greatest common factor from each group: \[ x(x+4) - 8(x+4). \] 7. Factor out the common binomial factor \((x+4)\): \[ (x+4)(x-8). \] Thus, the correct choice is A with the factored form: \[ x^{2}-4x-32=(x+4)(x-8). \]