What is a polynomial function in standard form with zeros 1, 2, -2 and -3

The zeros of the polynomial are 1, 2, -2 and -3, so this polynomial must have at least one of each of these factors:

(x-1), (x-2), (x-(-2)), and (x-(-3)); rewriting: (x-1), (x-2), (x+2), and (x+3).

Thus, any such polynomial must have a factor (x-1)(x-2)(x+2)(x+3).

The simplest such polynomial we can think of, is p(x)=(x-1)(x-2)(x+2)(x+3).

To write in standard form, lets first multiply the factors two by two as follows:

by the difference of squares formula, 

.

Next, we multiply our results:



.

 

The answer would be choice b