The function is .

The factors are and .

Perform the synthetic division method to test each factor.

Synthetic division for factor .

The divisor is in the form of

 When is divided by  The remainder is  .

 So is a factor.

.

The obtained depressed polynomial is .

Now test the second factor , with the depressed polynomial .

Synthetic division for factor .

The divisor is in the form of

The remainder is .

Because the remainder is not , when the depressed polynomial is divided by the factor ,

is not a factor of .

Since is a factor of , the quotient can be written in the factored form as

.