Solve the polynomial inequality.
-$( x + 9 ) ( x + 3 ) ( x - 4 )

Question

Solve the polynomial inequality.
-$( x + 9 ) ( x + 3 ) ( x - 4 ) < 0$
A) $( 4 , \infty )$
B) $( - 9 , - 3 ) \cup ( 4 , \infty )$
C) $( - \infty , - 9 ) \cup ( - 3,4 )$
D) $( - \infty , - 3 )$

Quizplus · Accepted Answer

To solve the inequality $( x + 9 ) ( x + 3 ) ( x - 4 ) < 0$, we find the zeros of the polynomial, which are $x = -9$, $x = -3$, and $x = 4$. These divide the real number line into four intervals: $(-\infty, -9)$, $(-9, -3)$, $(-3, 4)$, and $(4, \infty)$. Testing values from each interval in the inequality shows that the polynomial is negative in the intervals $(-\infty, -9)$ and $(-3, 4)$, making option C correct.

Solve the Polynomial Inequality (x+9)(x+3)(x−4)<0( x + 9 ) ( x + 3 ) ( x - 4 ) < 0(x+9)(x+3)(x−4)<0

Solve the Polynomial Inequality $( x + 9 ) ( x + 3 ) ( x - 4 ) < 0$