Question

factor the trinomial completely by factoring out

(4x^2 + 16x - 48)

select the correct choice below and fill in any answer

a. (4x^2 + 16x - 48 =)

b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Factor out the GCF

$$ 4x^2 + 16x - 48 = 4(x^2 + 4x - 12) $$

Step 2: Factor the remaining trinomial

Find two numbers that multiply to \(-12\) and add to \(4\):

$$ 6 \text{ and } -2 $$

$$ x^2 + 4x - 12 = (x + 6)(x - 2) $$

Step 3: Combine the factors

$$ 4(x + 6)(x - 2) $$

Answer:

A. \(4x^2 + 16x - 48 = 4(x + 6)(x - 2)\)