# How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 1, -2, -4?

Oct 1, 2016

$\textcolor{g r e e n}{{x}^{4} + 2 {x}^{3} - 13 {x}^{2} - 14 x + 24}$

#### Explanation:

If the polynomial has zeros at
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{3} , \textcolor{b l u e}{1} , \textcolor{m a \ge n t a}{- 2} , \textcolor{\mathmr{and} a n \ge}{- 4}$
then it has factors
color(white)("XXX")(x-color(red)(3)), (x-color(blue)1), (x-color(magneta)(""(-2))), (x-color(orange)(""(-4)))

$\left(x - 3\right) \cdot \left(x - 1\right) \cdot \left(x + 2\right) \cdot \left(x + 4\right)$

$\textcolor{w h i t e}{\text{XXXXXXXXX}} = {x}^{4} + 2 {x}^{3} - 13 {x}^{2} - 14 x + 24$