The function is .

Identify Possible Rational Zeros of :

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.

The polynomial function is .

Use rational zero theorem to find the potential rational zeros of a polynomial function.

If  is the rational zero, then  is factor of the constant term  and  is factor of the leading coefficient .

The possible values of  are .

The possible values of  are .

Now form all possible ratios of  are . 

The function is .

The function .

So, perform synthetic substitution method by testing .

The depressed polynomial is .

 is a one of factor of the function .

is a zero of .

Find the roots of the polynomial by using quadratic formula.

Quadratic formula: .

Compare with standard quadratic form .

.

Solution:

.

Therefore, and are also the factors of .

are complex zeros of .

Factor form of is .

The complex zeros are .

Factor form of is .