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