# How do you find all zeros of #F(x)= x^3 -8x^2 +25x -26#?

##### 1 Answer

There are three solutions:

#### Explanation:

The *rational root theorem* tells us that rational roots to a polynomial equation with integer coefficients can be written in the form

The polynomial equation is

The integer factors of the constant

The integer factors of the leading coefficient

The rational solutions must therefore be among the following:

Try each answer by substituting them into

Now we know that

*(Polynomial divison might need its own explanation for those who haven't learned it. If there's a separate Socratic thread on it, it should be linked here.)*

With the factorized polynomial

A quadratic equation

Plug

Now we have found all three solutions: