The function below has at least one rational zero.
Use this fact to find all zeros of the function.

If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

To find the rational zeros of the function , we can apply the Rational Root Theorem. This theorem suggests that any rational zero, in the form , has as a factor of the constant term (-14), and as a factor of the leading coefficient (3).

The factors of -14 are: ±1, ±2, ±7, ±14, and the factors of 3 are: ±1, ±3. So, the possible rational zeros are: ±1, ±2, ±7, ±14, ±1/3, ±2/3, ±7/3, ±14/3.

Testing these values, we find that is a root:

Now, we can factor using synthetic division by :

Next, we need to find the roots of . We can apply the Rational Root Theorem again. By testing , we found:

Trying :

Then attempting leads to another root:

Using synthetic division again, we can simplify this polynomial.

After calculations, the final factorization leads to:

The zeros of the function are:

Thus, the exact values of the zeros are: