Solve. Provide answers in interval notation.
-$(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)0$
A) $(-\infty, 1)$
B) $(5, \infty)$
C) $(-\infty,-8) \cup(1,5)$
D) $(-8,1) \cup(5, \infty)$

Question

Solve. Provide answers in interval notation.
-$(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)>0$
A) $(-\infty, 1)$
B) $(5, \infty)$
C) $(-\infty,-8) \cup(1,5)$
D) $(-8,1) \cup(5, \infty)$

Quizplus · Accepted Answer

To solve the inequality $(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)>0$, we find the zeros of the polynomial, which are $\mathrm{c}=-8$, $\mathrm{c}=1$, and $\mathrm{c}=5$. These values divide the number line into four intervals: $(-\infty, -8)$, $(-8, 1)$, $(1, 5)$, and $(5, \infty)$. Testing values from each interval in the inequality shows that the inequality is satisfied for $(-8, 1)$ and $(5, \infty)$, hence the solution in interval notation is $(-8,1) \cup(5, \infty)$.

Solve Provide Answers in Interval Notation (c+8)(c−1)(c−5)>0(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)>0(c+8)(c−1)(c−5)>0 A) (−∞,1)(-\infty, 1)(−∞,1) B) (5,∞)(5, \infty)(5,∞)

Solve Provide Answers in Interval Notation $(\mathrm{c}+8)(\mathrm{c}-1)(\mathrm{c}-5)>0$ A) $(-\infty, 1)$ B) $(5, \infty)$