# How do you use the rational roots theorem to find all possible zeros of x^3-x^2-4x+4?

Aug 20, 2016

$\textcolor{g r e e n}{x \in \left\{- 2 , + 1 , + 2\right\}}$
(see below for use of the Rational Root Theorem)

#### Explanation:

The Rational Root Theorem tells us that the rational zeros of

$\textcolor{red}{1} {x}^{3} - {x}^{2} - 4 x + \textcolor{b l u e}{4}$
are the factors of $\frac{\textcolor{b l u e}{4}}{\textcolor{red}{1}}$

Checking each of the possible factors we get:

which gives us zeros for

$x = - 2 , x = 1 , \mathmr{and} x = 2$

Since ${x}^{3} - {x}^{2} - 4 x + 4$ is of degree $3$
it can have a maximum of $3$ zeros
and we have found them all.