Answer
$P(x)=x^4-8x^3+14x^2+8x-15$
Work Step by Step
RECALL:
If $c$ is a zero of a polynomial, then $x-c$ is a factor of the polynomial.
Since -1, 1, 3, and 5 are zeros of the polynomial, then
$(x+2), (x-1), (x-3), \text{ and } (x-5)$ are factors of the polynomial.
Thus, one polynomial of degree 4 with the given zeros is:
$\\P(x) =(x+1)(x-1)(x-3)(x-5)
\\P(x)=x^4-8x^3+14x^2+8x-15$