Find the polynomial function.

Degree of the function is .

Distinct real zeros : .

Multiplicity : .

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Since the degree of the polynomial function is , it is an even function.

The leading coefficient() of the polynomial function must be negative.

Because for even and negative the end behavior of the polynomial function is and .

Let the three distinct real zeroes are and .

Then the factors are , and .

Since one factor has multiplicity , raise to the second power.

From the given data conclude that, there are two zeros that are not real.

Let be a factor, because has no real zeros.

Thus, the polynomial function is .

Graph the function :

Graph :

The polynomial function is .

Graph of the function is :

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