Answer
0 of multiplicity two
16 of multiplicity one
See graph below.
Work Step by Step
The question asks for all real zeros of P(x), their respective multiplicities, and the graph of P(x)
Given $P(x) = x^3 - 16x$
$P(x) = x(x^2 - 16)$
$P(x) = x(x-4)(x+4)$
Set $P(x) = 0$
Thus x = -4, 0, 4
To determine multiplicity, it is the power of the root determined from setting P(x) = 0
-4, 0, and 4 of multiplicity one
See graph below.
