Answer:
[tex]f(x)=x^{4}-7x^{2}+3x^{3}-27x-18[/tex]
Step-by-step explanation:
The polynomial function can be found by multiplying all roots. We know the four zeros, which we can express like this:
[tex]f(x)=(x+1)(x+2)(x+3)(x-3)[/tex]
Now, we multiple to find the expression:
[tex]f(x)=(x^{2}+2x+x+2)(x^{2}-9)\\f(x)=x^{4}-9x^{2}+2x^{3}-18x+x^{3}-9x+2x^{2}-18\\f(x)=x^{4}-7x^{2}+3x^{3}-27x-18[/tex]
Therefore the polynomial function with those four zeros is:
[tex]f(x)=x^{4}-7x^{2}+3x^{3}-27x-18[/tex]
