Convert to Interval Notation (x-5)(x-2)(x+1)>0

Problem

(x−5)*(x−2)*(x+1)>0

Solution

1. Identify the zeros of the polynomial by setting each factor equal to zero.

(x−5)*(x−2)*(x+1)=0

x=5,x=2,x=−1

2. Determine the intervals created by these zeros on the number line.

(−∞,−1),(−1,2),(2,5),(5,∞)

3. Test a value from each interval in the inequality (x−5)*(x−2)*(x+1)>0 to check the sign.
   For (−∞,−1) test x=−2 (−7)*(−4)*(−1)=−28<0 (Negative)
   For (−1,2) test x=0 (−5)*(−2)*(1)=10>0 (Positive)
   For (2,5) test x=3 (−2)*(1)*(4)=−8<0 (Negative)
   For (5,∞) test x=6 (1)*(4)*(7)=28>0 (Positive)

4. Select the intervals where the product is greater than zero (positive).

(−1,2)∪(5,∞)

Final Answer

(x−5)*(x−2)*(x+1)>0⇒(−1,2)∪(5,∞)

Want more problems? Check here!