# What is a cubic polynomial function in standard form with zeros 5, 2, and -5?

Mar 30, 2016

$f \left(x\right) = {x}^{3} - 2 {x}^{2} - 25 x + 50$

#### Explanation:

$f \left(x\right) = \left(x - 5\right) \left(x + 5\right) \left(x - 2\right)$

$= \left({x}^{2} - 25\right) \left(x - 2\right)$

$= {x}^{3} - 2 {x}^{2} - 25 x + 50$

Standard form sorts the powers of $x$ (or whatever variable you are using) in descending order.

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