Question

factor the trinomial completely. 6x³ + 36x² + 48x

Explanation:

Step1: Factor out GCF

Identify and factor the greatest common factor (GCF) of all terms. The GCF of $6x^3$, $36x^2$, and $48x$ is $6x$.
$6x^3 + 36x^2 + 48x = 6x(x^2 + 6x + 8)$

Step2: Factor quadratic trinomial

Factor the quadratic $x^2 + 6x + 8$ by finding two numbers that multiply to 8 and add to 6 (these numbers are 2 and 4).
$x^2 + 6x + 8 = (x + 2)(x + 4)$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1.
$6x(x^2 + 6x + 8) = 6x(x + 2)(x + 4)$

Answer:

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