$\"\"$

The function is $\"\"$ .

Identify Possible Rational Zeros :

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

$\"\"$ .

Possible rational zeros $\"\"$ .

$\"\"$

Therefore, the possible rational zeros of $\"\"$ are $\"\"$ .

$\"\"$

Consider $\"\"$ .

Perform the synthetic substitution method by testing $\"\"$ .

$\"\"$

Since $\"\"$ , conclude that $\"\"$ is a zero of $\"\"$ .

Therefore, $\"\"$ is a rational zero.

The depressed polynomial is $\"\"$ .

The depressed polynomial $\"\"$ yields no rational zeros.

Therefore, $\"\"$ is a rational zero of $\"\"$ .

$\"\"$

Therefore the possible rational zeros of $\"\"$ are $\"\"$ .

The rational zero of $\"\"$ is $\"\"$ .