Question

factor this polynomial expression, and then write it in its fully factored form.

(3x^3 + 3x^2 - 18x)

select the correct answer.

• (3x(x - 3)(x + 2))
• ((3x^2 + 9x)(x - 2))
• (3x(x^2 + x - 6))
• (3x(x + 3)(x - 2))

Explanation:

Factor out the greatest common factor

$$ 3x^3 + 3x^2 - 18x = 3x(x^2 + x - 6) $$

Factor the remaining quadratic trinomial

$$ x^2 + x - 6 = (x + 3)(x - 2) $$

Combine factors into fully factored form

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

Answer:

• (A) \(3x(x - 3)(x + 2)\)
• (B) \((3x^2 + 9x)(x - 2)\)
• (C) \(3x(x^2 + x - 6)\)
• (D) \(3x(x + 3)(x - 2)\) (Correct answer)