How do you solve (x2)(x+1)(x5)0 using a sign chart?

1 Answer
Nov 25, 2017

Solution: 1x<2andx5or[1,2][5,)

Explanation:

f(x)=(x2)(x+1)(x5)0 . Crititical numbers

are x=1,x=2,x=5. Since at those numbers f(x)=0

Sign chart:

When x<1 sign of (x2)(x+1)(x5) is ()()()=();<0

When 1<x<2 sign of (x2)(x+1)(x5) is ()(+)()=(+);>0

When 2<x<5 sign of (x2)(x+1)(x5) is (+)(+)()=();<0

When x>5 sign of (x2)(x+1)(x5) is (+)(+)(+)=(+);>0

Solution: 1x<2andx5or[1,2][5,)

graph{(x-2)(x+1)(x-5) [-40, 40, -20, 20]} [Ans]