Select a possible formula for the polynomial $f(x)$, given that $f(x)$ has degree three, $f(-3)=f(4)=f(7)=0$, and $\lim_{x\to \infty}f(x)=-\infty$.

A. $(x + 3)(x + 4)(x-7)$
B. $-(x + 3)(x + 7)(x + 4)$
C. $-(x + 3)(x-4)(x-7)$
D. $-(x + 3)^2 (x-4)(x-7)$

Is there more than one possible solution?

A. Yes, because there could be different multiplicities for the roots.
B. No, because there is only one function that meets all of the requirements.
C. No, because we know the three roots and it is a degree three polynomial.
D. Yes, because the leading coefficient could be any negative number.

Hint: