Answer:
C
Step-by-step explanation:
Given the inequality
(x - 3)(x + 5) ≤ 0
Find the zeros by equating to zero
(x - 3)(x + 5) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 5 = 0 ⇒ x = - 5
Thus the domain is split into 3 intervals
--------------------------------------------------------------
- ∞ < x ≤ - 5 → (1)
- 5 ≤ x ≤ 3 → (2)
3 ≤ x < + ∞ → (3)
Select a test point in each interval and check validity
x = - 10 → (- 13)(- 5) = 65 > 0 ← not valid
x = 0 → (- 3)(5) = - 15 < 0 ← valid
x = 10 → (7)(15) = 105 > 0 ← not valid
Solution is { x | - 5 ≤ x ≤ 3 }
