We are to find a polynomial f(x) of degree 4 that has the following zeros.
-5, 9 (multiplicity 2), 0
So,
The degree 4 polynomial of the given zeros is:
But recall, that there is a multiplicity which tells the number of times a factor occurs
So, x = 9 occurred twice.
Therefore, the degree 4 polynomial of the given zeros:
f(x) = x(x + 5)(x - 9)(x - 9)
So in a factored form:
f(x) = x(x + 5)(x - 9)(x - 9)