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

The greatest common factor (GCF) of \(3x^3\), \(3x^2\), and \(-18x\) is \(3x\). Factoring out \(3x\) gives:
\(3x(x^2 + x - 6)\)

Step2: Factor the quadratic

Factor \(x^2 + x - 6\). We need two numbers that multiply to \(-6\) and add to \(1\). These numbers are \(3\) and \(-2\). So:
\(x^2 + x - 6 = (x + 3)(x - 2)\)

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1:
\(3x(x + 3)(x - 2)\)

Answer:

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