Completely factor the polynomial or state that the polynomial is prime.
-$$x ^ { 3 } + 40 x ^ { 2 } + 400 x$$
A) $x ( x + 20 ) ( x - 20 )$
B) prime
C) $x ( x + 20 ) ^ { 2 }$
D) $x ( x - 20 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The polynomial can be factored by first taking out the common factor of $x$, resulting in $x(x^2 + 40x + 400)$. Recognizing that $40x + 400$ can be rewritten as $20^2 + 2 \cdot 20 \cdot x + x^2$, it becomes clear that the expression inside the parentheses is a perfect square trinomial, $(x + 20)^2$. Therefore, the completely factored form is $x(x + 20)^2$.

Completely Factor the Polynomial or State That the Polynomial Is x3+40x2+400xx ^ { 3 } + 40 x ^ { 2 } + 400 xx3+40x2+400x

Completely Factor the Polynomial or State That the Polynomial Is $x ^ { 3 } + 40 x ^ { 2 } + 400 x$