Solve the polynomial inequality. Express the solution in interval notation.
-$x ^ { 3 } - 2 x ^ { 2 } - 35 x 0$
A) $( - 5 , \infty )$
B) $( - 5,0 ) \cup ( 7 , \infty )$
C) $( - \infty , - 5 ) \cup ( 0,7 )$
D) $( - 7,0 ) \cup ( 5 , \infty )$

Question

Solve the polynomial inequality. Express the solution in interval notation.
-$x ^ { 3 } - 2 x ^ { 2 } - 35 x > 0$
A) $( - 5 , \infty )$
B) $( - 5,0 ) \cup ( 7 , \infty )$
C) $( - \infty , - 5 ) \cup ( 0,7 )$
D) $( - 7,0 ) \cup ( 5 , \infty )$

Quizplus · Accepted Answer

First, factor the polynomial: $x^3 - 2x^2 - 35x = x(x^2 - 2x - 35) = x(x + 5)(x - 7)$. The roots are $x = 0$, $x = -5$, and $x = 7$. Test values in each interval determined by these roots to see where the polynomial is positive: $x < -5$, $-5 < x < 0$, $0 < x < 7$, and $x > 7$. The polynomial is positive for $x$ in the intervals $(-5, 0)$ and $(7, \infty)$, leading to the solution in interval notation as $(-5, 0) \cup (7, \infty)$.

Solve the Polynomial Inequality x3−2x2−35x>0x ^ { 3 } - 2 x ^ { 2 } - 35 x > 0x3−2x2−35x>0

Solve the Polynomial Inequality $x ^ { 3 } - 2 x ^ { 2 } - 35 x > 0$