Question

A polynomial has been factored as `f(x)=(x-6)(x+5)(x-9)`, what are the zeros of the polynomial?

Answer 1

`x = 6`, `x = -5` or `x = 9`

Explanation:

`f(x) = (x-6)(x+5)(x-9)`

If all of the linear factors are non-zero, then so is their product `f(x)`.

If any of the linear factors is zero, then so is their product `f(x)`.

So the zeros of `f(x)` are precisely the values of `x` which make at least one of the linear factors `0`, namely: `6`, `-5` or `9`.