$\"\"$

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 $\"\"$ and $\"\"$ .

The possible values of $\"\"$ are $\"\"$ .

Now form all possible ratios of $\"\"$ are $\"\"$ and $\"\"$ .

$\"\"$

Make a table for the synthetic division and test possible zeros.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Since $\"image\"$ , $\"image\"$ is one of the zero of the function.

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: $\"\"$ .

Substitute $\"image\"$ , $\"image\"$ and $\"image\"$ in the above expression.

$\"\"$

Therefore, $\"\"$ and $\"\"$ are also the factors of $\"\"$ .

Therefore roots of $\"\"$ are $\"\"$ and $\"\"$ .

$\"\"$ are complex zeros of $\"\"$ .

$\"\"$

The complex zeros are $\"\"$ .

Factor form of $\"\"$ is $\"image\"$ .