# How do you write a polynomial function with the given zeros 1, 7, -5?

Mar 21, 2016

$f \left(x\right) = {x}^{3} - 3 {x}^{2} - 33 x + 35$

#### Explanation:

The simplest polynomial with these zeros is:

$f \left(x\right) = \left(x - 1\right) \left(x - 7\right) \left(x + 5\right)$

$= \left({x}^{2} - 8 x + 7\right) \left(x + 5\right)$

$= {x}^{3} - 3 {x}^{2} - 33 x + 35$

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