(х+2)(х+4)(х-1)>0

Предыдущий
вопрос Следующий
вопрос

To solve this inequality, we need to first find the critical points by setting each factor equal to zero:

(x + 2) = 0
x = -2

(x + 4) = 0
x = -4

(x - 1) = 0
x = 1

So, the critical points are x = -2, x = -4, and x = 1.

Next, we can test each interval created by the critical points by plugging in a test point:

Test x = -5: (-5 + 2)(-5 + 4)(-5 - 1) = (-3)(-1)(-6) = 18, which is greater than 0.Test x = -3: (-3 + 2)(-3 + 4)(-3 - 1) = (-1)(1)(-4) = 4, which is greater than 0.Test x = 0: (0 + 2)(0 + 4)(0 - 1) = (2)(4)(-1) = -8, which is not greater than 0.Test x = 2: (2 + 2)(2 + 4)(2 - 1) = (4)(6)(1) = 24, which is greater than 0.

Therefore, the solution to the inequality (x + 2)(x + 4)(x - 1) > 0 is x < -4 or -2 < x < 1.