Inequality problem: (x-1)(x+2)(x-4)<0

[jshaziza]

(x-1)(x+2)(x-4)<0

x=1, x=-2, x=4

I than used a chart to determine the signs of the factors by listing in what regions each factor was negative and positive on the number line. The signs of the product that I got was --|+|--|+. What I can't understand from my book is how they take this information and than put into interval or set notation for the problem. Could someone please take me over the steps so I can understand this? Thx. for your help.

 

[arthur ohlsten]

[x-1][x+2][x-4]<0
let us look at [x-1][x+2][x-4]=0

the curve crosses the x axis at x=1,-2,and 4
at x=0 the curves value is 8

at x=-infinity the curve is -infinity
at x=infinity the curve is at infinity

now we will look at[x-1][x+2][x-4]<0
where is [x-1][x+2][x-4]<0 ?

-infinity<x<-2 and 1<x<4 answer

hope this helps
Arthur