Question

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

Answer 1

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)

Answer 2

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