Question

warm-up
select the correct answer.
factor this polynomial expression, and then write it in its fully factored form.
$3x^3 + 3x^2 - 18x$
$\circ$ $3x(x - 3)(x + 2)$
$\circ$ $(3x^2 + 9x)(x - 2)$
$\circ$ $3x(x^2 + x - 6)$
$\circ$ $3x(x + 3)(x - 2)$

Explanation:

Step1: Factor out GCF

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

Step2: Factor quadratic trinomial

Factor the quadratic expression $x^2 + x - 6$ 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:

3x(x + 3)(x - 2)