Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$5 x ^ { 5 } + 10 x ^ { 4 } y - 75 x ^ { 3 } y ^ { 2 }$$
A) $5 x ^ { 3 } ( x - 3 y ) ( x + 5 y )$
B) $\left( 5 x ^ { 2 } + 15 x y \right) \left( x ^ { 3 } - 5 y \right)$
C) $( x - 3 y ) \left( 5 x ^ { 4 } + 25 x y \right)$
D) $5 x ^ { 3 } ( x + 3 y ) ( x - 5 y )$

Question

Quizplus · Accepted Answer

The polynomial can be factored by first taking out the greatest common factor, $5x^3$, resulting in $5x^3(x^2 + 2xy - 15y^2)$. The quadratic $x^2 + 2xy - 15y^2$ can be factored further into $(x - 3y)(x + 5y)$.

Factor Completely 5x5+10x4y−75x3y25 x ^ { 5 } + 10 x ^ { 4 } y - 75 x ^ { 3 } y ^ { 2 }5x5+10x4y−75x3y2

Factor Completely $5 x ^ { 5 } + 10 x ^ { 4 } y - 75 x ^ { 3 } y ^ { 2 }$