Question

What are all the rational zeroes of `f(x) = x^3 - 3x^2 - 4x + 12`?

Answer 1

The rational zeros are `x = 2`, `x = -2` and `x = 3`

Explanation:

Factor by grouping:

`f(x) = x^3-3x^2-4x+12`

`=(x^3-3x^2)-(4x-12)`

`=x^2(x-3)-4(x-3)`

`=(x^2-4)(x-3)`

`=(x-2)(x+2)(x-3)`

So the rational zeros are `x = 2`, `x = -2` and `x = 3`