# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -2, -4, -7?

##### 1 Answer
Dec 5, 2016

The zeros are: $\textcolor{red}{- 2} , \textcolor{b l u e}{- 4}$ and $\textcolor{g r e e n}{- 7}$

Find the factors of the function in the form of $\left(x + z\right)$

The first factor:-
$z \textcolor{red}{- 2} = 0$
$z = 2$

$\left(x + 2\right)$

The second factor:-
$z \textcolor{b l u e}{- 4} = 0$
$z = 4$

$\left(x + 4\right)$

The third factor:-
$z \textcolor{g r e e n}{- 7} = 0$
$z = 7$

$\left(x + 7\right)$

Multiply the factors to get the least-degree function

$\left(x + 2\right) \left(x + 4\right) \left(x + 7\right) = \left({x}^{2} + 4 x + 2 x + 8\right) \left(x + 7\right)$

$= \left({x}^{2} + 6 x + 8\right) \left(x + 7\right)$

$= {x}^{3} + 7 {x}^{2} + 6 {x}^{2} + 42 x + 8 x + 56$

Combine like terms

$f \left(x\right) = {x}^{3} + 13 {x}^{2} + 50 x + 56$