# Write a polynomial function of least degree with integral coefficients that has the given zeros ? -2 mult. 3

## I don't understand what the mult. means.

Jul 9, 2018

$p \left(x\right) = {x}^{3} + 6 {x}^{2} + 12 x + 8$

#### Explanation:

$\text{since "x=-2" is a zero, then}$

$\left(x + 2\right) \text{ is a factor of the polynomial}$

$\text{given "x=-2" of mult. 3 then}$

$\left(x + 2\right) \left(x + 2\right) \left(x + 2\right) \text{ are the factors of the polynomial}$

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

$\textcolor{w h i t e}{\times x} = {x}^{3} + 6 {x}^{2} + 12 x + 8$
graph{x^3+6x^2+12x+8 [-10, 10, -5, 5]}