Answer: (-∞, -2) U (1, ∞)
Explanation:
x² + x - 2 > 0
First, find the zeros by setting the equation EQUAL to zero:
x² + x - 2 = 0
(x + 2)(x - 1) = 0
x + 2 = 0 x - 1 = 0
x = -2 x = 1
Next, choose a test point to the left, between, and to the right of the zeros and check to see if the test points are positive (greater than zero)
Left (x = -3): (-3 + 2)(-3 - 1) = (-)(-) = +
Between (x = 0): (0 + 2)(0 - 1) = (+)(-) = -
Right (x = 2): (2 + 2)(2 - 1) = (+)(+) = +
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The left and right test points are positive (greater than zero) so the solution is x < -2 and x > 1
Interval Notation: (-∞, -2) U (1, ∞)