Question

factor the trinomial completely. if the trinomial contains a greatest common factor (other than 1), factor it out first.

(2x^2 + 26x + 80)

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

a. (2x^2 + 26x + 80 = \\)
(factor completely.)

b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor out the greatest common factor (GCF)

$$ 2x^2 + 26x + 80 = 2(x^2 + 13x + 40) $$

Step 2: Factor the remaining trinomial

Find two numbers that multiply to \(40\) and add to \(13\):

$$ 8 \times 5 = 40 $$

$$ 8 + 5 = 13 $$

Write the factored form of the trinomial:

$$ x^2 + 13x + 40 = (x + 8)(x + 5) $$

Step 3: Combine all factors

$$ 2(x + 8)(x + 5) $$

Answer:

A. \(2x^2 + 26x + 80 = 2(x + 8)(x + 5)\)