The function is .

The zero is .

Synthetic Substitition :

Perfom the synthetic substitution method to verify is a zero of .

The depressed polynomial is .

Since is a zero of , also a  zero of .

Perfom the synthetic substitution method to verify on the obtained depressed polynomial.

Therefore and are the factors of .

Using these zeros and the new depressed polynomial from the last division, we can write

.

Finding Rational Zeros :

The remaining depressed polynomial is .

To find the rational zeros use the quadratic formula .

Consider  .

Here .

Substiute the values in the quadratic formula .

The zeros of the depressed polynomial are .

Therefore and are the rational zeros.

Therefore, are the factors of .

By using Factor theorem,

When  then   is a factor of polynomial.

Factored form of .

So has four real zeros.

Zeros are .

The linear factorization of is  .

Zeros are .