Question

question 12 of 15
submit test
25-26 pre-college mathematics - semester...
question 1-12
factor completely:
$3x^2 + 15x + 18$
\\(\bigcirc\\) $3(x^2 + 5x + 6)$
\\(\bigcirc\\) $(3x + 9)(x + 2)$
\\(\bigcirc\\) $3(x + 3)(x + 2)$
\\(\bigcirc\\) $(x + 3)(3x + 5)$

Explanation:

Step1: Factor out the GCF

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

Step2: Factor the quadratic

Next, factor the quadratic \(x^2 + 5x + 6\). We need two numbers that multiply to \(6\) and add to \(5\). These numbers are \(3\) and \(2\), so:
\(x^2 + 5x + 6 = (x + 3)(x + 2)\)

Step3: Combine the factors

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

Answer:

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