Step 1: \ \

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.

The equation is $\"\"$ .

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

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

Step 2: \ \

Consider $\"\"$ .

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

$\"\"$

By using synthetic substitution, it can be determined that $\"\"$ is a rational zero.

The depressed polynomial is $\"\"$ .

Step 3:

Consider $\"\"$ .

Perform the synthetic substitution method on the depressed polynomial by testing $\"\"$ .

$\"\"$

By using synthetic substitution, it can be determined that $\"\"$ is a rational zero.

The new depressed polynomial is $\"\"$ .

Step 4:

Consider $\"\"$ . \ \

$\"\"$

Therefore $\"\"$ are the factors of the equation.

Step 5:

The final quotient can be written as $\"\"$ .

Factoring the quadratic expression yeilds $\"\"$ .

Zeros are $\"\"$ . \ \

Solution:

The zeros of the equation are $\"\"$ .