Question

factor the trinomial completely.

(x^2 + 13x + 11)

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

a. (x^2 + 13x + 11 = \\) (type your answer in factored form.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify factoring requirements

To factor a trinomial of the form \(x^2 + bx + c\), find two integers that multiply to \(c\) and add up to \(b\).

For \(x^2 + 13x + 11\):

• Multiply to \(c = 11\)
• Add to \(b = 13\)

Step 2: Test factors of 11

Since \(11\) is a prime number, its only positive integer factors are \(1\) and \(11\).

$$ 1 \cdot 11 = 11 $$

$$ 1 + 11 = 12 eq 13 $$

No two integers multiply to \(11\) and add up to \(13\). Therefore, the trinomial cannot be factored over the integers.

Answer:

B. The polynomial is prime.