Question

factor completely:
$3x^2 + 15x + 18$
$\circ \\ 3\left(x^2 + 5x + 6\
ight)$
$\circ \\ \left(3x + 9\
ight)\left(x + 2\
ight)$
$\circ \\ 3\left(x + 3\
ight)\left(x + 2\
ight)$
$\circ \\ \left(x + 3\
ight)\left(3x + 5\
ight)$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(3x^2\), \(15x\), and \(18\). The GCF of 3, 15, and 18 is 3. So factor out 3:
\(3x^2 + 15x + 18 = 3(x^2 + 5x + 6)\)

Step2: Factor the quadratic

Now factor the quadratic \(x^2 + 5x + 6\). We need two numbers that multiply to 6 and add to 5. Those numbers are 2 and 3. So:
\(x^2 + 5x + 6 = (x + 2)(x + 3)\)

Step3: Combine the factors

Substitute the factored quadratic back into the expression from Step 1:
\(3(x^2 + 5x + 6) = 3(x + 2)(x + 3)\) or \(3(x + 3)(x + 2)\)

Answer:

\(3(x + 3)(x + 2)\) (corresponding to the option \(3(x + 3)(x + 2)\))