Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$6 x ^ { 3 } - 48$
A) $6 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$
B) $6 ( x - 12 ) \left( x ^ { 2 } + 12 x + 24 \right)$
C) $6 ( x - 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$
D) $6 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor, which is 6, giving $6(x^3 - 8)$. Recognizing $x^3 - 8$ as a difference of cubes, it can be factored as $(x - 2)(x^2 + 2x + 4)$, leading to the complete factorization $6(x - 2)(x^2 + 2x + 4)$.

Factor the Polynomial Completely 6x3−486 x ^ { 3 } - 486x3−48

Factor the Polynomial Completely $6 x ^ { 3 } - 48$