Factor the trinomial, or state that the trinomial is prime.
\[
x^{2}-4 x-12
\]

Select the correct choice below and fill in any answer boxes within your choice.
A. $x^{2}-4 x-12=$
B. The polynomial is prime.

Answer

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Answer

$\boxed{x^{2}-4x-12 = (x - 6)(x + 2)}$ is the final answer.

Steps

Step 1 ：The given trinomial is $x^{2}-4x-12$. We need to factorize it.

Step 2 ：We are looking for two numbers that multiply to -12 (the constant term) and add to -4 (the coefficient of the x term).

Step 3 ：The numbers that satisfy these conditions are -6 and 2 because $(-6) * 2 = -12$ and $-6 + 2 = -4$.

Step 4 ：So, we can write the trinomial as: $x^{2}-4x-12 = (x - 6)(x + 2)$.

Step 5 ：$\boxed{x^{2}-4x-12 = (x - 6)(x + 2)}$ is the final answer.