# Math Help - Rational Zeros Theorem

1. ## Rational Zeros Theorem

I have been given the equation:

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

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?

2. Originally Posted by Shonard
I have been given the equation:

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

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?
The possible zeros are of the form $\frac{p}{q}$ where $p$ represents all the numbers that divide -80, and $q$ represents all the integers that divide 81.

This particular expression is a nightmare. Try $\frac{-4}{9}$

3. Awesome that worked.

I now have:

$(x + 4/9)(81x^3 + 36x^2 - 405x - 180)$

unfortunately this sequence is about as easy to work with as the first, is there any way to narrow down the possibility's?