If a polynomial function has a zero of 3, then one of its factors is (x - 3).
If there is only one zero and the degree of the polynomial is 4, then we simply have to raise the factor (x - 3) by 4.
So, the polynomial function is f(x) = (x - 3)⁴.
[tex]f(x)=(x-3)^4[/tex]