Identify Possible Rational Zeros:

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 function is .

The function have no positive real zeros, because there is no change of signs.

Because the leading coefficient is , the possible rational zeros are the integer factors of the constant term .

Therefore, the possible rational zeros of are .

The function is .

The function .

So, perform synthetic substitution method by testing .

The depressed polynomial is .

Therefore, is the factor 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 .

The complex zeros are .

By the factor theorem, the factor form of .

.

Factor form of is .

The complex zeros are .

Factor form of is .