# What are all the possible rational zeros for f(x)=5x^3-2x^2+20x-8?

Oct 2, 2016

The possible rational zeros are: $\pm 1 , \pm 2 , \pm 4 , \pm 8 , \pm \frac{1}{5} , \pm \frac{2}{5} , \pm \frac{4}{5} , \pm \frac{8}{5}$

#### Explanation:

Find the possible rational zeros of:

$f \left(x\right) = \textcolor{red}{5} {x}^{3} - 2 {x}^{2} + 2 - x - \textcolor{b l u e}{8}$

The possible rational zeros are found by dividing the factors of the constant term $\textcolor{b l u e}{8}$ (called $\textcolor{b l u e}{p}$) by the factors of the leading coefficient $\textcolor{red}{5}$ (called $\textcolor{red}{q}$).

$\frac{\textcolor{b l u e}{p}}{\textcolor{red}{q}} = \frac{\pm 1 , 2 , 4 , 8}{\pm 1 , 5}$

Dividing each number in the numerator by each number in the denominator gives:

$\pm 1 , \pm 2 , \pm 4 , \pm 8 , \pm \frac{1}{5} , \pm \frac{2}{5} , \pm \frac{4}{5} , \pm \frac{8}{5}$