Question

factor the polynomial completely. if the polynomial is prime, so state.

\\ -x^2 - 14x - 49 \\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. \\( -x^2 - 14x - 49 = \\)

b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor out the negative sign

$$ -x^2 - 14x - 49 = -(x^2 + 14x + 49) $$

Step 2: Factor the trinomial

$$ x^2 + 14x + 49 = (x + 7)(x + 7) = (x + 7)^2 $$

Step 3: Combine factors

$$ -(x + 7)^2 $$

Answer:

A. \( -x^2 - 14x - 49 = -(x + 7)^2 \)