Question

select the correct answer.

what is the completely factored form of this polynomial?

(2x^5 + 12x^3 - 54x)

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

Explanation:

Factor out the greatest common factor

$$ 2x^5 + 12x^3 - 54x = 2x(x^4 + 6x^2 - 27) $$

Factor the quadratic in terms of \(x^2\)

$$ x^4 + 6x^2 - 27 = (x^2 + 9)(x^2 - 3) $$

Combine factors into final form

$$ 2x(x^2 - 3)(x^2 + 9) $$

Answer:

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