$\"\"$

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.

$\"\"$

Because the leading coefficient is $\"\"$ , the possible rational zeros are the integer factors of the constant term $\"\"$ .

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

$\"\"$

$\"\"$ .

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

$\"\"$

$\"\"$ is a rational zero.

The depressed polynomial is $\"\"$ .

The final quotient is $\"\"$ .

The factor $\"\"$ yields no rational zeros.

Rational zero of $\"\"$ is $\"\"$ .

$\"\"$

Possible rational zeros of $\"\"$ are $\"\"$ and $\"\"$ .

Rational zero of $\"\"$ is $\"\"$ .