By inspection you can see that if x=1, y=-1-1+2=0, so x=1 is an x-intercept.
To find more x intercepts (if any) divide by the zero 1 using synthetic division:
1 | -1 0 -1 2
-1 -1 -1 | -2
-1 -1 -2 | 0 =-x2-x-2.
x2+x=-2, x2+x+¼=-2+¼, (x+½)2=-7/4 which has no real solutions (no real square root of a negative number). So x=1 is the only x-intercept.