The function is .

The factors are and .

Perform the synthetic division method to test each factor.

Synthetic division for factor .

Now the divisor is in the form of .

.

When is divided by , the remainder is  .

So is a factor of  .

The depressed polynomial is .

The obtained depressed polynomial is .

Now test the second factor with the depressed polynomial .

Now the divisor is in the form of .

.

When is divided by , the remainder is  .

So is a factor of .

Both and are the factors of .

The remaining cubic factor can be written as .

The quotient in factored form as .

and are factors of the polynomial. \ \

.