# Precalculus : Find the Zeros of a Function Using the Rational Zeros Theorem

## Example Questions

### Example Question #1 : Find The Zeros Of A Function Using The Rational Zeros Theorem

Use the Rational Zero Theorem to find all potential rational zeros of the polynomial . Which of these is NOT a potential zero?

Explanation:

To find the potential rational zeros by using the Rational Zero Theorem, first list the factors of the leading coefficient and the constant term:

Constant 24: 1, 2, 3, 4, 6, 8, 12, 24

Now we have to divide every factor from the first list by every factor of the second:

Removing duplicates [for example, and are both equivalent to 1] gives us the following list:

The only choice not on this list is .

### Example Question #2 : Find The Zeros Of A Function Using The Rational Zeros Theorem

Consider the polynomial . Of the potential rational zeros provided by the Rational Zero Theorem, which can we determine to NOT be a solution?

Explanation:

The potential zeros must have a factor of -15 as their numerator and a factor of 6 as their denominator. This eliminates  as a possibility since 6 is not a factor of -15.

Now we need to test which of these values actually give zero when plugged into the polynomial.

First, :

Now :

Finally :

Since this one doesn't give us zero, it is not a solution of the polynomial.