Question

factor this polynomial expression.
$2x^2 + 12x + 18$
a. $2(x+3)(x+3)$
b. $(2x+9)(x+2)$
c. $2(x+3)(x-3)$
d. $2(x-3)(x-3)$

Explanation:

Step1: Factor out the GCF

Factor 2 from each term:
$2(x^2 + 6x + 9)$

Step2: Factor the quadratic trinomial

Identify perfect square trinomial:
$x^2 + 6x + 9 = (x+3)^2 = (x+3)(x+3)$

Step3: Combine the factors

Substitute back into the expression:
$2(x+3)(x+3)$

Answer:

A. $2(x+3)(x+3)$