The polynomial function is .

Graph :

Draw a coordinate plane.

Graph the function .

The graph of the function is :

Observe the graph :

The solid dots represent the roots of the polynomial function.

From the graph   and are the roots.

So and are the factors of given polynomial function.

The polynomial 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 .

The remainder is .

So is a factor of .

Now test the second factor with the obtained depressed factor  .

Synthetic division for factor .

The divisor is in the form of .

The remainder is .

So is a factor of .

The depressed polynomial is .

Graph :

The graph of the depressed polynomial  is :

Observe the graph :

The solid dot represent the root of the polynomial function.

From the graph  is the root.

So is the factor of  .

Now test the factor with the obtained depressed factor  .

Synthetic division for factor .

The divisor is in the form of .

Because the remainder when the depressed polynomial is divided by is .

is a repeated factor of .

So is a factor of .

The quotient can be written as .

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