# How do you write a polynomial in standard form given zeros 5, -4 and 1?

Apr 7, 2016

#### Answer:

$f \left(x\right) = {x}^{3} - 2 {x}^{2} - 19 x + 20$

#### Explanation:

Convert each zero into a linear factor to define:

$f \left(x\right) = \left(x - 5\right) \left(x + 4\right) \left(x - 1\right) = {x}^{3} - 2 {x}^{2} - 19 x + 20$

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