Answer
$x=-1,2,3$
Work Step by Step
Step 1. The coefficients of the dividend $f(x)$ can be identified in order as $\{1,-4,1,6\}$ 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 $f(x)=(x^2-5x+6)(x+1)=(x-3)(x-2)(x+1)$; thus we can find the zeros of $f(x)$ as $x=-1,2,3$
