Question

How do you find all zeros of the function `f(x) = x^3 + x^2 - 12x`?

Answer 1

`f(x)` has zeros `x=0`, `x=-4` and `x=3`

Explanation:

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

Note that `4*3 = 12` and `4-3=1`

Hence we find:

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

So `f(x)` has zeros `x=0`, `x=-4` and `x=3`