## Precalculus: Mathematics for Calculus, 7th Edition

$P(x)=x^4-4x^3-4x^2+16x$
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: $\\P(x) =(x+2)(x)(x-2)(x-4) \\P(x)=x^4-4x^3-4x^2+16x$