Factor completely: $x ^ { 4 } - 24 x ^ { 2 } - 25$
A) $\left( x ^ { 2 } + 25 \right) ( x - 1 ) ( x + 1 )$
B) $( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 1 \right)$
C) $( x - 5 ) ( x + 5 ) ( x - 1 ) ( x + 1 )$
D) $( x - 5 ) ( x + 5 ) ( x + 1 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

This expression can be factored by recognizing it as a quadratic in form, $x^4 - 24x^2 - 25$, which resembles $a^2 - 2ab - 25$. By substituting $x^2$ for $a$, it becomes $(x^2)^2 - 24(x^2) - 25$, which factors as $(x^2 - 25)(x^2 + 1)$ or $(x - 5)(x + 5)(x^2 + 1)$, matching option B.

Factor Completely x4−24x2−25x ^ { 4 } - 24 x ^ { 2 } - 25x4−24x2−25

Factor Completely $x ^ { 4 } - 24 x ^ { 2 } - 25$