# How do you write an equation of a polynomials with zeros: -3,0, 4; degree 3?

Dec 6, 2017

$p \left(x\right) = {x}^{3} - {x}^{2} - 12 x$

#### Explanation:

$\text{given the zeros of a polynomial say}$

$x = a , x = b \text{ and } x = c$

$\text{then the factors are "(x-a),(x-b)" and } \left(x - c\right)$

$\text{the polynomial is the product of the factors}$

$\Rightarrow p \left(x\right) = k \left(x - a\right) \left(x - b\right) \left(x - c\right) \leftarrow \textcolor{b l u e}{\text{k is a multiplier}}$

$\text{here "x=-3,x=0,x=4larrcolor(blue)"zeros}$

$\Rightarrow \left(x + 3\right) , \left(x - 0\right) \text{ and "(x-4)" are the factors}$

$\text{letting } k = 1$

$p \left(x\right) = x \left(x + 3\right) \left(x - 4\right)$

$\textcolor{w h i t e}{p \left(x\right)} = x \left({x}^{2} - x - 12\right)$

$\textcolor{w h i t e}{p \left(x\right)} = {x}^{3} - {x}^{2} - 12 x \leftarrow \textcolor{b l u e}{\text{is a possible polynomial}}$