Question

How do you solve `(x-1)(x-2)(x-3)<=0` using a sign chart?

Answer 1

The answer is `x in ] -oo,1 ] uu [2, 3]`

Explanation:

Let `f(x)=(x-1)x-2)(x-3)`

Let's do the sign chart
`color(white)(aaaaa)` `x` `color(white)(aaaaa)` `-oo` `color(white)(aaaaa)` `1` `color(white)(aaaaa)` `2` `color(white)(aaaaa)` `3` `color(white)(aaaaa)` `+oo`
`color(white)(aaaaa)` `x-1` `color(white)(aaaaa)` `-` `color(white)(aaaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aaa)` `+`
`color(white)(aaaaa)` `x-2` `color(white)(aaaaa)` `-` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaa)` `+`
`color(white)(aaaaa)` `x-3` `color(white)(aaaaa)` `-` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaa)` `+`
`color(white)(aaaaa)` `f(x)` `color(white)(aaaaaa)` `-` `color(white)(aaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaa)` `+`