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

Jan 4, 2017

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

#### Explanation:

$f \left(x\right) = \left(x - 6\right) \left(x + 5\right) \left(x - 9\right)$

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

If any of the linear factors is zero, then so is their product $f \left(x\right)$.

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