First of all, note, that 0 is neither a positive nor a negative number.

**Quote:**

… what if the answer is 0. Then (*x* – 4)(*x* – 3)(*x* + 2)(*x* + 1) = 0 which will deny the question stem.

Indeed, when

*x* equals 4, 3, -2, or -1, then the whole expression will be 0, which answers the main question with "NO".

When we combine the both statements together none of the above values are possible.