Factor completely.
-$$\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96$$
A) $\left( x ^ { 2 } + 4 \right) ( x + 4 ) ^ { 2 }$
B) $\left[ x ^ { 2 } + 4 \right) ( x + 4 ) ( x - 4 )$
C) $\left( x ^ { 2 } - 4 \right) ( x + 4 ) ( x - 4 )$
D) $x ^ { 4 } - 12 x ^ { 2 } - 64$

Question

Quizplus · Accepted Answer

The given expression can be rewritten as a quadratic in terms of $y = x^2 - 4$, resulting in $y^2 - 4y - 96$. Factoring this quadratic gives $(y - 12)(y + 8)$. Substituting back $x^2 - 4$ for $y$, we get $(x^2 - 4 - 12)(x^2 - 4 + 8)$, which simplifies to $(x^2 - 16)(x^2 + 4)$, or $(x + 4)(x - 4)(x^2 + 4)$.

Factor Completely (x2−4)2−4(x2−4)−96\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96(x2−4)2−4(x2−4)−96

Factor Completely $\left( x ^ { 2 } - 4 \right) ^ { 2 } - 4 \left( x ^ { 2 } - 4 \right) - 96$