# What are all the possible rational zeros for #f(x)=2x^3+x^2+8x+4# and how do you find all zeros?

##### 1 Answer

One rational zero at

#### Explanation:

The Rational Root Theorem tells us that given a function of the form:

all rational zeroes will be of the form:

We can test all such possibilities (I would suggest using a spread sheet as below) for

This gives us that there is only one rational zero at

which implies

Using long division or synthetic division (with

For zeroes of the given function we have: