# How do you write a polynomial function that has the zeros 2, -1, 0?

Nov 7, 2016

Polynomial function that has the zeros $2$, $- 1$ and $0$ is ${x}^{3} - {x}^{2} - 2 x$

#### Explanation:

A polynomial function with zeros $\alpha$ (multiplicity $p$), $\beta a$ (multiplicity $q$) and $\gamma$ (multiplicity $r$) is

${\left(x - \alpha\right)}^{p} {\left(x - \beta\right)}^{q} {\left(x - \gamma\right)}^{r}$

Hence, a polynomial function that has the zeros $2$, $- 1$ and $0$ (multiplicity not mentioned and hence $1$) is

$\left(x - 2\right) \left(x - \left(- 1\right)\right) \left(x - 0\right) = x \left(x + 1\right) \left(x - 2\right) = x \left({x}^{2} - 2 x + x - 2\right) = {x}^{3} - {x}^{2} - 2 x$