The solution set of ( x-1) ( x+2) > 0 isa.[-2 ,1 ]b.( - ∞, 1 ) u ( 2 , ∞)c.∅d.( - ∞, -2) u ( 1 , ∞)

To find the solution set of the inequality (x - 1)(x + 2) > 0, we first find the critical points by setting each factor equal to zero:

x - 1 = 0 => x = 1 x + 2 = 0 => x = -2

These are the points where the expression changes sign. We can test the intervals (-∞, -2), (-2, 1), and (1, ∞) by choosing a test point in each interval and substituting it into the inequality.

For (-∞, -2), let's choose x = -3: (-3 - 1)(-3 + 2) = (-4)(-1) = 4 > 0

For (-2, 1), let's choose x = 0: (0 - 1)(0 + 2) = (-1)(2) = -2 < 0

For (1, ∞), let's choose x = 2: (2 - 1)(2 + 2) = (1)(4) = 4 > 0

Therefore, the solution set of the inequality is the union of the intervals (-∞, -2) and (1, ∞), which is represented as d. ( - ∞, -2) u ( 1 , ∞).