Answer
$P(x)=x^4-4x^3-4x^2+16x$
Work Step by Step
RECALL:
If $c$ is a zero of a polynomial, then $x-c$ is a factor of the polynomial.
Since -2, 0, 2, and 4 are zeros of the polynomial, then
$(x+2), (x), (x-2), \text{ and } (x-4)$ are factors of the polynomial.
Thus, one polynomial of degree 3 with the given zeros is:
$\\P(x) =(x+2)(x)(x-2)(x-4)
\\P(x)=x^4-4x^3-4x^2+16x$
