How many zeros are in - 5x (x-3) (x^2-16)

This is a fourth degree polynomial, so by the fundamental theorem of algebra, there are four zeroes, whether they are complex or real.

The expression can be rational factorized into

-5x (x-3) (x+4) (x-4), so all four factors (hence zeroes) are real.

Answer: There are four real zeroes in - 5x (x-3) (x^2-16)

Count the number of times x is used as a factor of this polynomial. I count 4. Thus, this expression will have 4 zeros.