# How do you use the rational root theorem to find the roots of #x^3-x^2+2x-2#?

##### 1 Answer

**Answer**: The root of this polynomial is

The Rational Roots Theorem says that:

- if
#P(x)# is a polynomial with integer coefficients - and
#p/q# is a root of#P# (i.e.#P(p/q) = 0# ),

then

In our case,

First, let's write down **all the factors of the constant term**:

Next, let's write down **all the factors of the leading coefficient**:

Now, let's write down the possible values of

It can be easily verified that the only

(We can check this result by factoring P(x) as

A graphical illustration can be seen below, by plotting the corresponding function:

graph{x^3 - x^2 + 2x - 2 [-10, 10, -5, 5]}