Convert to Interval Notation x^3-36x>0

Problem

x3−36*x>0

Solution

1. Factor the polynomial by taking out the greatest common factor, which is x

x*(x2−36)>0

2. Factor further using the difference of squares formula, a2−b2=(a−b)*(a+b) where a=x and b=6

x*(x−6)*(x+6)>0

3. Identify the critical points by setting each factor equal to zero.

x=0

x−6=0⇒x=6

x+6=0⇒x=−6

4. Test intervals created by the critical points (−6,0,6) to see where the expression is positive.

• For (−∞,−6) let x=−7 (−7)*(−13)*(−1)=−91<0

• For (−6,0) let x=−1 (−1)*(−7)*(5)=35>0

• For (0,6) let x=1 (1)*(−5)*(7)=−35<0

• For (6,∞) let x=7 (7)*(1)*(13)=91>0

5. Select the intervals where the expression is strictly greater than zero.

(−6,0)∪(6,∞)

Final Answer

x3−36*x>0⇒(−6,0)∪(6,∞)

Want more problems? Check here!