x f(x)

____________

-5 0

-1 36

0 0

1 6

2 0

The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following could define f?

A) (x – 5) (x + 2)

B) (x + 5)^2 (x – 2)^3

C) x^2 (x + 5) (x – 2)^2

D) x (x + 5) (x – 2)

Specifically, can you explain why C is correct but D cannot be?