Question

How do you use the rational roots theorem to find all possible zeros of `x^3-x^2-4x+4`?

Answer 1

`color(green)(x in {-2, +1, +2})`
(see below for use of the Rational Root Theorem)

Explanation:

The Rational Root Theorem tells us that the rational zeros of

`color(red)(1)x^3-x^2-4x+color(blue)(4)`
are the factors of `(color(blue)(4))/(color(red)(1))`

Checking each of the possible factors we get:

which gives us zeros for

`x=-2, x=1, and x=2`

Since `x^3-x^2-4x+4` is of degree `3`
it can have a maximum of `3` zeros
and we have found them all.