Question

explain how you would factor $2x^2 + 8x + 6 = 0$

select the correct choice below, and fill in the answer box(es) to complete your choice.

a. there is no common factor, so factor the trinomial to get $\boldsymbol{\square}=0$

b. first factor out a common factor of $\boldsymbol{\square}$. then factor the trinomial to get $\boldsymbol{\square}=0$

Explanation:

Step1: Factor out common term

Identify GCD of $2x^2, 8x, 6$ is 2:
$2x^2 + 8x + 6 = 2(x^2 + 4x + 3)$

Step2: Factor the quadratic trinomial

Find two numbers that multiply to 3 and add to 4 (1 and 3):
$x^2 + 4x + 3 = (x+1)(x+3)$

Step3: Combine factors

Substitute back to get fully factored form:
$2(x+1)(x+3)=0$

Answer:

B. First factor out a common factor of 2. Then factor the trinomial to get $2(x+1)(x+3)=0$