# How do you write a polynomial in standard form given the zeros x=3,1,2and -2?

Jul 1, 2016

$f \left(x\right) = {x}^{4} - 4 {x}^{3} - {x}^{2} + 16 x - 12$

#### Explanation:

$f \left(x\right) = \left(x - 3\right) \left(x - 1\right) \left(x - 2\right) \left(x + 2\right)$

$= \left(x - 3\right) \left(x - 1\right) \left({x}^{2} - 4\right)$

$= \left(x - 3\right) \left({x}^{3} - {x}^{2} - 4 x + 4\right)$

$= {x}^{4} - 4 {x}^{3} - {x}^{2} + 16 x - 12$

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