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 of the polynomial.

.

The obtained depressed polynomial is .

Now test the second factor , with the depressed polynomial .

Synthetic division for factor .

Rewrite the division expression so that the divisor is in the form of .

.

The obtained divisor is .

The divisor is in the form of .

.

When is divided by  , the remainder is  .

So is not a factor of  .

Since is a factor of , the quotient in the factored form is .

is a factor of the polynomial.

is not a factor of the polynomial.

Factored form of polynomial is .