Solve the polynomial inequality.
-$$( x + 8 ) \left( x ^ { 2 } - 25 \right) 0$$
A) $( - 8 , - 5 ) \cup ( 5 , \infty )$
B) $( - \infty , - 5 ) \cup ( 5 , \infty )$
C) $( - \infty , 5 ) \cup ( 5,8 )$
D) $( - 8,5 )$

Question

Solve the polynomial inequality.
-$$( x + 8 ) \left( x ^ { 2 } - 25 \right) > 0$$
A) $( - 8 , - 5 ) \cup ( 5 , \infty )$
B) $( - \infty , - 5 ) \cup ( 5 , \infty )$
C) $( - \infty , 5 ) \cup ( 5,8 )$
D) $( - 8,5 )$

Quizplus · Accepted Answer

To solve the inequality $( x + 8 ) ( x ^ { 2 } - 25 ) > 0$, factor the quadratic expression to get $(x + 8)(x + 5)(x - 5) > 0$. The critical points are at $x = -8$, $x = -5$, and $x = 5$. Test intervals around these points to determine where the expression is positive. The solution intervals are $(-8, -5)$ and $(5, \infty)$.

Solve the Polynomial Inequality (x+8)(x2−25)>0( x + 8 ) \left( x ^ { 2 } - 25 \right) > 0(x+8)(x2−25)>0

Solve the Polynomial Inequality $( x + 8 ) \left( x ^ { 2 } - 25 \right) > 0$