# How do you write a polynomial in standard form given the zeros x= -1, 3, 5?

Aug 17, 2016

$f \left(x\right) = {x}^{3} - 7 {x}^{2} + 7 x + 15$

#### Explanation:

Each zero corresponds to a linear factor...

$f \left(x\right) = \left(x - \left(- 1\right)\right) \left(x - 3\right) \left(x - 5\right)$

$= \left(x + 1\right) \left(x - 3\right) \left(x - 5\right)$

$= {x}^{3} - 7 {x}^{2} + 7 x + 15$

This is in standard form, with the terms arranged in descending degree.

Any polynomial in $x$ with these zeros will be a multiple (scalar or polynomial) of this $f \left(x\right)$.