Convert to Interval Notation x^2>2x+8

Problem

x2>2*x+8

Solution

1. Rearrange the inequality to one side so that the right side is zero.

x2−2*x−8>0

2. Factor the quadratic expression on the left side.

(x−4)*(x+2)>0

3. Identify the critical points by setting the factors equal to zero.

x−4=0⇒x=4

x+2=0⇒x=−2

4. Test the intervals created by the critical points: (−∞,−2) (−2,4) and (4,∞)
   For x=−3 (−3−4)*(−3+2)=(−7)*(−1)=7>0 (True)
   For x=0 (0−4)*(0+2)=(−4)*(2)=−8>0 (False)
   For x=5 (5−4)*(5+2)=(1)*(7)=7>0 (True)

5. Select the intervals where the inequality is true.

x<−2* or *x>4

Final Answer

x2>2*x+8=(−∞,−2)∪(4,∞)

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