Question

select the correct answer.

what is the completely factored form of this polynomial?

(5x^4 + 20x^3 - 105x^2)

(5x^3(x - 3)(x + 7))
(5x^3(x + 3)(x - 7))
(5x^2(x + 3)(x - 7))
(5x^2(x - 3)(x + 7))

Explanation:

Factor out the greatest common factor

$$ 5x^4 + 20x^3 - 105x^2 = 5x^2(x^2 + 4x - 21) $$

Factor the remaining quadratic trinomial

$$ x^2 + 4x - 21 = (x - 3)(x + 7) $$

Combine the factored components

$$ 5x^4 + 20x^3 - 105x^2 = 5x^2(x - 3)(x + 7) $$

Answer:

• (A) \(5x^3(x - 3)(x + 7)\)
• (B) \(5x^3(x + 3)(x - 7)\)
• (C) \(5x^2(x + 3)(x - 7)\)
• (D) \(5x^2(x - 3)(x + 7)\) (Correct answer)