The function is .

Rewrite the function as .

The factor is .

Perform the synthetic division to find .

The divisor is in the form of .

Where , which is the root.

Write the terms of the dividend so that the degrees of the terms are in descending order.

Then write just the coefficients as shown below.

Write the constant of the divisor   to the left.

In this case, . Bring the first coefficient, , down.

Multiply the sum,   by  : .

Write the product under the next coefficient,  and add: .

Multiply the sum,   by :.

Write the product under the next coefficient, and add .

The remainder is the last entry in the last row.

Therefore, the remainder .

Let .

.

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 intezer factors of the constant term .

or .

Therefore, the possible rational zeros of are .

The function is .

Perform the synthetic substitution method by testing and .

The remainder.

Therefore is not a factor of .

The remainder.

Therefore is a factor of .

The depressed polynomial is .

Perform the synthetic substitution method on the depressed polynomial by testing and .

The remainder.

Therefore is not a factor of .

The remainder.

Therefore, is not a factor of .

The possible rational zeros of are .

The rational zero of is .

The possible rational zeros of are .

The rational zero of is .

The value of .