Question

factor the trinomial completely.

\\ -x^2 + 13x + 30 \\

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

a. \\( -x^2 + 13x + 30 = \\) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor out the negative sign

$$ -x^2 + 13x + 30 = -(x^2 - 13x - 30) $$

Step 2: Factor the trinomial inside the parentheses

Find two numbers that multiply to \(-30\) and add to \(-13\):

$$ -15 \cdot 2 = -30 $$

$$ -15 + 2 = -13 $$

Write the factored form:

$$ -(x - 15)(x + 2) $$

Answer:

A. \(-x^2 + 13x + 30 = -(x - 15)(x + 2)\)