# How do you use the rational root theorem to list all possible roots for x^3+81x^2-49x-49=0?

Oct 9, 2016

The list of all possible rational roots is $\pm 1 , \pm 7. \pm 49$

#### Explanation:

$\textcolor{b l u e}{1} {x}^{3} + 81 {x}^{2} - 49 x - \textcolor{red}{49} = 0$

The rational roots theorem says that the list of POSSIBLE rational roots is the factors of the constant $\textcolor{red}{49}$ divided by the factors of the leading coefficient $\textcolor{b l u e}{1}$.

The factors of the constant are known as $\textcolor{red}{p}$ and the factors of the leading coefficient are known as $\textcolor{b l u e}{q}$.

$\frac{\textcolor{red}{p}}{\textcolor{b l u e}{q}} = \frac{\pm 1 , \pm 7 , \pm 49}{\pm 1} = \pm 1 , \pm 7 , \pm 49$