Question

factor this polynomial expression, and then write it in its fully factored form.
3x³ + 3x² - 18x
select the correct answer.
○ 3x(x - 3)(x + 2)
○ (3x² + 9x)(x - 2)
○ 3x(x² + x - 6)
○ 3x(x + 3)(x - 2)

Explanation:

Step1: Factor out GCF

Identify the greatest common factor (GCF) of all terms, which is $3x$.
$3x^3 + 3x^2 - 18x = 3x(x^2 + x - 6)$

Step2: Factor quadratic trinomial

Factor the quadratic $x^2 + x - 6$ by finding two numbers that multiply to $-6$ and add to $1$ (these numbers are $3$ and $-2$).
$x^2 + x - 6 = (x + 3)(x - 2)$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1.
$3x(x^2 + x - 6) = 3x(x + 3)(x - 2)$

Answer:

D. $3x(x + 3)(x - 2)$