# How do you write a polynomial function in standard form with the given zeros: -1, 3, 5?

Mar 6, 2016

The simplest such (non-zero) polynomial is:

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

#### Explanation:

As a product of linear factors, we can define:

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

$= \left(x + 1\right) \left({x}^{2} - 8 x + 15\right)$

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

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