Question

factor the trinomial completely.

\\x^2 - 6x - 27\\

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

a. \\(x^2 - 6x - 27 = \\) (type your answer in factored form.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

Identify the coefficients of the trinomial \( x^2 - 6x - 27 \):

$$ a = 1, \quad b = -6, \quad c = -27 $$

Step 2: Find factors

Find two numbers that multiply to \( c = -27 \) and add to \( b = -6 \):

$$ -9 \cdot 3 = -27 $$

$$ -9 + 3 = -6 $$

Step 3: Write factored form

Write the trinomial in its factored form \( (x + p)(x + q) \):

$$ (x - 9)(x + 3) $$

Answer:

A. \( x^2 - 6x - 27 = (x - 9)(x + 3) \)