Question

How do you solve and write the following in interval notation: `(b + 4)(b - 1)(b - 3) <0`?

Answer 1

The solution is `b in ]-oo,-4[uu]1,3[`

Explanation:

Let `f(b)=(b+4)(b-1)(b-3)`

Let's build a sign chart

`color(white)(aaaa)` `b` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-4` `color(white)(aaaa)` `1` `color(white)(aaaa)` `3` `color(white)(aaaaa)` `+oo`

`color(white)(aaaa)` `b+4` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `b-1` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `b-3` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `f(b)` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

Therefore

`f(b)<` when `b in ]-oo,-4[uu]1,3[`