Answer:
(- ∞, - 4 ] ∪ [7, + ∞ )
Explanation:
Determine the zeros by equating to zero, that is
x² - 3x - 28 = 0 ← in standard form
(x - 7)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 4 = 0 ⇒ x = - 4
The zeros divide the domain into 3 intervals
(- ∞ , - 4 ], [ - 4, 7 ], [ 7, + ∞)
Choose a test point in each interval and compare value with required solution
x = - 5 : (- 5)² - 3(- 5) - 28 = 25 + 15 - 28 = 12 > 0
x = 0 : 0 - 0 - 28 = - 28 < 0
x = 10 : 10² - 3(10) - 28 = 100 - 30 - 28 = 42 > 0
Solutions are the first and third interval, that is
x ∈ (- ∞, - 4 ] ∪ [ - 7, + ∞)