# How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^3-7x^2+x-7#?

##### 1 Answer

#### Explanation:

The sign pattern of

The sign pattern of

The rational roots theorem tells us that we can find all rational roots to a polynomial by dividing

We also don't need to bother checking the negative roots, since Descartes' rule of signs told us there are no negative roots.

After checking

Now we can solve for when the second factor equals

Now that we have all the zeroes we can see that our original conclusions with Descartes' rule were correct. We only got