# What are all the possible rational zeros for #f(x)=3x^3-x^2-3x+1# and how do you find all zeros?

##### 1 Answer

#### Explanation:

The pattern of signs of

The pattern of signs for

The rational roots theorem states that we can find all possible rational roots to a polynomial by dividing

I'll begin by trying the negative values since I know for a fact the polynomial has a real root. Of these, we find that

This means we can bring out a factor of

We can factor this quadratic by grouping:

We can use the zero factor principle to find that the remaining roots are