I have been given the equation:

$\displaystyle f(x) = 81x^7 + 72x^6 - 389x^5 - 360x^4 - 80x^3$

and asked to find a) and b) using the Rational Zeros Theorem

a) Factor f(x) into linear factors.

b) List the zeros of f(x) and their multiplicities

I understand that to use the rational zeroes theorem requires that there is a constant term so I factor out x^3, but at that point it seems there are no rational zeros. Any thoughts?