# How do you write a polynomial in standard form given the zeros x=-4, 5. -1?

May 26, 2016

${x}^{3} - 21 x - 20 = 0$

#### Explanation:

If $\left\{\alpha , \beta , \gamma , \delta , . .\right\}$ are the zeros of a function, then the function is

$\left(x - \alpha\right) \left(x - \beta\right) \left(x - \gamma\right) \left(x - \delta\right) \ldots = 0$

Here zeros are $- 4$, $5$) and $- 1$, hence function is

$\left(x - \left(- 4\right)\right) \left(x - 5\right) \left(x - \left(- 1\right)\right) = 0$ or

$\left(x + 4\right) \left(x - 5\right) \left(x + 1\right) = 0$ or

$\left({x}^{2} + 4 x - 5 x - 20\right) \left(x + 1\right) = 0$ or

$\left({x}^{2} - x - 20\right) \left(x + 1\right) = 0$ or

${x}^{3} - {x}^{2} - 20 x + {x}^{2} - x - 20 = 0$ or

${x}^{3} - 21 x - 20 = 0$