Factor the expression completely. If the expression is prime, so indicate. $- 3 x ^ { 3 } + 81$
A) $- 3 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$
B) $- 3 ( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$
C) $- 3 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$
D) $- 3 ( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$
E) prime

Question

Quizplus · Accepted Answer

We can factor out -3 first, giving us $-3(x^3 - 27)$. Notice that $x^3 - 27$ can be rewritten as $(x^3 - 3^3)$. This is a factorable difference of cubes, which we can factor into $(x - 3)(x^2 + 3x + 9)$. Therefore, the expression completely factored is $-3(x-3)(x^2+3x+9)$. The other answer choices do not work because they either do not have the correct factors or they have incorrect signs.

Factor the Expression Completely −3x3+81- 3 x ^ { 3 } + 81−3x3+81

Factor the Expression Completely $- 3 x ^ { 3 } + 81$