Question

factor the trinomial completely.

\\x^2 - 15x + 26\\

select the correct choice below and fill in any answer boxes within your choice.

a. \\(x^2 - 15x + 26 = \\)

b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify coefficients

For the trinomial \( x^2 - 15x + 26 \):

$$ a = 1, \quad b = -15, \quad c = 26 $$

Step 2: Find factors

We need two numbers that multiply to \( c = 26 \) and add to \( b = -15 \).

Factors of \( 26 \):

$$ -1 \times -26 = 26 \implies -1 + (-26) = -27 $$

$$ -2 \times -13 = 26 \implies -2 + (-13) = -15 $$

The required numbers are \( -2 \) and \( -13 \).

Step 3: Write factored form

$$ x^2 - 15x + 26 = (x - 2)(x - 13) $$

Answer:

A. \( x^2 - 15x + 26 = (x - 2)(x - 13) \)