Question

factor the trinomial completely.

(x^2 - 11x + 18)

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

a. (x^2 - 11x + 18 =) (type your answer in factored form.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

Find two numbers that multiply to the constant term \(18\) and add up to the linear coefficient \(-11\).

$$ \text{Product} = 18 $$

$$ \text{Sum} = -11 $$

Step 2: Find the factors

Since the product is positive and the sum is negative, both numbers must be negative.

$$ -9 \times -2 = 18 $$

$$ -9 + (-2) = -11 $$

Step 3: Write in factored form

$$ (x - 9)(x - 2) $$

Answer:

A. \(x^2 - 11x + 18 =\) \((x - 9)(x - 2)\)