Answer:
f(x) = -5(x+3)(x+3)(x+3)(x-2)
Step-by-step explanation:
If the polynomial has three zeros in -3 and one zero in 2, the lowest degree we need is four, as the polynomial has these four zeros, so we can use a generic form of a fourth degree polynomial:
y = a(x-x1)(x-x2)(x-x3)(x-x4)
Where x1, x2, x3 and x4 are the zeros, so we have that:
y = a(x+3)(x+3)(x+3)(x-2)
Now, to find the value of the constant 'a', we need to use the information that f(0) = 270:
270 = a*3*3*3*(-2)
-54a = 270
a = -5
So the polynomial is:
f(x) = -5(x+3)(x+3)(x+3)(x-2)
