Chapter 5 - Polynomials and Polynomial Functions - 5-2 Polynomials, Linear Factors, and Zeros - Practice and Problem-Solving Exercises - Page 293: 23

$f(x)=x^3+2x^2-x-2$

RECALL: If $a$ is a zero of a polynomial, then $x−a$ is a factor of the polynomial. Thus, having $x=1, -1, -2$ as zeros of the polynomial function means that $x-1,x+1$, and $x+2$ are factors of the polynomial. Therefore the function is $f(x)=(x-1)(x+1)(x+2) \\f(x)=x^3+2x^2-x-2.$