Answer:
f(x) = -2(x +5)²(x -2)(x -4)
Step-by-step explanation:
When a polynomial has a zero of x=p, that means it has a factor of (x-p). The multiplicity of a zero corresponds to the exponent of that factor (the number of times it is a factor). The polynomial can be made to include a specific point by choosing a vertical scale factor. Here, that is represented by 'a'.
Your polynomial will be ...
f(x) = a(x +5)²(x -2)(x -4)
We want f(3) = 128, so ...
128 = a(3 +5)²(3 -2)(3 -4) = -64a
-2 = a . . . . . divide by -64
The function is then ...
f(x) = -2(x +5)²(x -2)(x -4)
