Chapter 2 - Section 2.4 - Dividing Polynomials; Remainder and Factor Theorems - Exercise Set - Page 364: 42

$x=-1,1,2$

Step 1. The coefficients of the dividend $f(x)$ can be identified in order as $\{1,-2,-1,2\}$ and the divisor is $x+1$; use synthetic division as shown in the figure to get the quotient and the remainder. Step 2. We can identify the result as $f(x)=(x^2-3x+2)(x+1)=(x-1)(x-2)(x+1)$; thus we can find the zeros of $f(x)$ as $x=-1,1,2$